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• Comparative Analysis

What It Is and Why It's Useful

Comparative analysis asks writers to make an argument about the relationship between two or more texts. Beyond that, there's a lot of variation, but three overarching kinds of comparative analysis stand out:

• Coordinate (A ↔ B): In this kind of analysis, two (or more) texts are being read against each other in terms of a shared element, e.g., a memoir and a novel, both by Jesmyn Ward; two sets of data for the same experiment; a few op-ed responses to the same event; two YA books written in Chicago in the 2000s; a film adaption of a play; etc. 
• Subordinate (A  → B) or (B → A ): Using a theoretical text (as a "lens") to explain a case study or work of art (e.g., how Anthony Jack's The Privileged Poor can help explain divergent experiences among students at elite four-year private colleges who are coming from similar socio-economic backgrounds) or using a work of art or case study (i.e., as a "test" of) a theory's usefulness or limitations (e.g., using coverage of recent incidents of gun violence or legislation un the U.S. to confirm or question the currency of Carol Anderson's The Second ).
• Hybrid [A  → (B ↔ C)] or [(B ↔ C) → A] , i.e., using coordinate and subordinate analysis together. For example, using Jack to compare or contrast the experiences of students at elite four-year institutions with students at state universities and/or community colleges; or looking at gun culture in other countries and/or other timeframes to contextualize or generalize Anderson's main points about the role of the Second Amendment in U.S. history.

"In the wild," these three kinds of comparative analysis represent increasingly complex—and scholarly—modes of comparison. Students can of course compare two poems in terms of imagery or two data sets in terms of methods, but in each case the analysis will eventually be richer if the students have had a chance to encounter other people's ideas about how imagery or methods work. At that point, we're getting into a hybrid kind of reading (or even into research essays), especially if we start introducing different approaches to imagery or methods that are themselves being compared along with a couple (or few) poems or data sets.

Why It's Useful

In the context of a particular course, each kind of comparative analysis has its place and can be a useful step up from single-source analysis. Intellectually, comparative analysis helps overcome the "n of 1" problem that can face single-source analysis. That is, a writer drawing broad conclusions about the influence of the Iranian New Wave based on one film is relying entirely—and almost certainly too much—on that film to support those findings. In the context of even just one more film, though, the analysis is suddenly more likely to arrive at one of the best features of any comparative approach: both films will be more richly experienced than they would have been in isolation, and the themes or questions in terms of which they're being explored (here the general question of the influence of the Iranian New Wave) will arrive at conclusions that are less at-risk of oversimplification.

For scholars working in comparative fields or through comparative approaches, these features of comparative analysis animate their work. To borrow from a stock example in Western epistemology, our concept of "green" isn't based on a single encounter with something we intuit or are told is "green." Not at all. Our concept of "green" is derived from a complex set of experiences of what others say is green or what's labeled green or what seems to be something that's neither blue nor yellow but kind of both, etc. Comparative analysis essays offer us the chance to engage with that process—even if only enough to help us see where a more in-depth exploration with a higher and/or more diverse "n" might lead—and in that sense, from the standpoint of the subject matter students are exploring through writing as well the complexity of the genre of writing they're using to explore it—comparative analysis forms a bridge of sorts between single-source analysis and research essays.

Typical learning objectives for single-sources essays: formulate analytical questions and an arguable thesis, establish stakes of an argument, summarize sources accurately, choose evidence effectively, analyze evidence effectively, define key terms, organize argument logically, acknowledge and respond to counterargument, cite sources properly, and present ideas in clear prose.

Common types of comparative analysis essays and related types: two works in the same genre, two works from the same period (but in different places or in different cultures), a work adapted into a different genre or medium, two theories treating the same topic; a theory and a case study or other object, etc.

How to Teach It: Framing + Practice

Framing multi-source writing assignments (comparative analysis, research essays, multi-modal projects) is likely to overlap a great deal with "Why It's Useful" (see above), because the range of reasons why we might use these kinds of writing in academic or non-academic settings is itself the reason why they so often appear later in courses. In many courses, they're the best vehicles for exploring the complex questions that arise once we've been introduced to the course's main themes, core content, leading protagonists, and central debates.

For comparative analysis in particular, it's helpful to frame assignment's process and how it will help students successfully navigate the challenges and pitfalls presented by the genre. Ideally, this will mean students have time to identify what each text seems to be doing, take note of apparent points of connection between different texts, and start to imagine how those points of connection (or the absence thereof)

• complicates or upends their own expectations or assumptions about the texts
• complicates or refutes the expectations or assumptions about the texts presented by a scholar
• confirms and/or nuances expectations and assumptions they themselves hold or scholars have presented
• presents entirely unforeseen ways of understanding the texts

—and all with implications for the texts themselves or for the axes along which the comparative analysis took place. If students know that this is where their ideas will be heading, they'll be ready to develop those ideas and engage with the challenges that comparative analysis presents in terms of structure (See "Tips" and "Common Pitfalls" below for more on these elements of framing).

Like single-source analyses, comparative essays have several moving parts, and giving students practice here means adapting the sample sequence laid out at the " Formative Writing Assignments " page. Three areas that have already been mentioned above are worth noting:

• Gathering evidence : Depending on what your assignment is asking students to compare (or in terms of what), students will benefit greatly from structured opportunities to create inventories or data sets of the motifs, examples, trajectories, etc., shared (or not shared) by the texts they'll be comparing. See the sample exercises below for a basic example of what this might look like.
• Why it Matters: Moving beyond "x is like y but also different" or even "x is more like y than we might think at first" is what moves an essay from being "compare/contrast" to being a comparative analysis . It's also a move that can be hard to make and that will often evolve over the course of an assignment. A great way to get feedback from students about where they're at on this front? Ask them to start considering early on why their argument "matters" to different kinds of imagined audiences (while they're just gathering evidence) and again as they develop their thesis and again as they're drafting their essays. ( Cover letters , for example, are a great place to ask writers to imagine how a reader might be affected by reading an their argument.)
• Structure: Having two texts on stage at the same time can suddenly feel a lot more complicated for any writer who's used to having just one at a time. Giving students a sense of what the most common patterns (AAA / BBB, ABABAB, etc.) are likely to be can help them imagine, even if provisionally, how their argument might unfold over a series of pages. See "Tips" and "Common Pitfalls" below for more information on this front.

Sample Exercises and Links to Other Resources

• Common Pitfalls
• Advice on Timing
• Try to keep students from thinking of a proposed thesis as a commitment. Instead, help them see it as more of a hypothesis that has emerged out of readings and discussion and analytical questions and that they'll now test through an experiment, namely, writing their essay. When students see writing as part of the process of inquiry—rather than just the result—and when that process is committed to acknowledging and adapting itself to evidence, it makes writing assignments more scientific, more ethical, and more authentic. 
• Have students create an inventory of touch points between the two texts early in the process.
• Ask students to make the case—early on and at points throughout the process—for the significance of the claim they're making about the relationship between the texts they're comparing.
• For coordinate kinds of comparative analysis, a common pitfall is tied to thesis and evidence. Basically, it's a thesis that tells the reader that there are "similarities and differences" between two texts, without telling the reader why it matters that these two texts have or don't have these particular features in common. This kind of thesis is stuck at the level of description or positivism, and it's not uncommon when a writer is grappling with the complexity that can in fact accompany the "taking inventory" stage of comparative analysis. The solution is to make the "taking inventory" stage part of the process of the assignment. When this stage comes before students have formulated a thesis, that formulation is then able to emerge out of a comparative data set, rather than the data set emerging in terms of their thesis (which can lead to confirmation bias, or frequency illusion, or—just for the sake of streamlining the process of gathering evidence—cherry picking). 
• For subordinate kinds of comparative analysis , a common pitfall is tied to how much weight is given to each source. Having students apply a theory (in a "lens" essay) or weigh the pros and cons of a theory against case studies (in a "test a theory") essay can be a great way to help them explore the assumptions, implications, and real-world usefulness of theoretical approaches. The pitfall of these approaches is that they can quickly lead to the same biases we saw here above. Making sure that students know they should engage with counterevidence and counterargument, and that "lens" / "test a theory" approaches often balance each other out in any real-world application of theory is a good way to get out in front of this pitfall.
• For any kind of comparative analysis, a common pitfall is structure. Every comparative analysis asks writers to move back and forth between texts, and that can pose a number of challenges, including: what pattern the back and forth should follow and how to use transitions and other signposting to make sure readers can follow the overarching argument as the back and forth is taking place. Here's some advice from an experienced writing instructor to students about how to think about these considerations:

a quick note on STRUCTURE

     Most of us have encountered the question of whether to adopt what we might term the “A→A→A→B→B→B” structure or the “A→B→A→B→A→B” structure.  Do we make all of our points about text A before moving on to text B?  Or do we go back and forth between A and B as the essay proceeds?  As always, the answers to our questions about structure depend on our goals in the essay as a whole.  In a “similarities in spite of differences” essay, for instance, readers will need to encounter the differences between A and B before we offer them the similarities (A d →B d →A s →B s ).  If, rather than subordinating differences to similarities you are subordinating text A to text B (using A as a point of comparison that reveals B’s originality, say), you may be well served by the “A→A→A→B→B→B” structure.  

     Ultimately, you need to ask yourself how many “A→B” moves you have in you.  Is each one identical?  If so, you may wish to make the transition from A to B only once (“A→A→A→B→B→B”), because if each “A→B” move is identical, the “A→B→A→B→A→B” structure will appear to involve nothing more than directionless oscillation and repetition.  If each is increasingly complex, however—if each AB pair yields a new and progressively more complex idea about your subject—you may be well served by the “A→B→A→B→A→B” structure, because in this case it will be visible to readers as a progressively developing argument.

As we discussed in "Advice on Timing" at the page on single-source analysis, that timeline itself roughly follows the "Sample Sequence of Formative Assignments for a 'Typical' Essay" outlined under " Formative Writing Assignments, " and it spans about 5–6 steps or 2–4 weeks. 

Comparative analysis assignments have a lot of the same DNA as single-source essays, but they potentially bring more reading into play and ask students to engage in more complicated acts of analysis and synthesis during the drafting stages. With that in mind, closer to 4 weeks is probably a good baseline for many single-source analysis assignments. For sections that meet once per week, the timeline will either probably need to expand—ideally—a little past the 4-week side of things, or some of the steps will need to be combined or done asynchronously.

What It Can Build Up To

Comparative analyses can build up to other kinds of writing in a number of ways. For example:

• They can build toward other kinds of comparative analysis, e.g., student can be asked to choose an additional source to complicate their conclusions from a previous analysis, or they can be asked to revisit an analysis using a different axis of comparison, such as race instead of class. (These approaches are akin to moving from a coordinate or subordinate analysis to more of a hybrid approach.)
• They can scaffold up to research essays, which in many instances are an extension of a "hybrid comparative analysis."
• Like single-source analysis, in a course where students will take a "deep dive" into a source or topic for their capstone, they can allow students to "try on" a theoretical approach or genre or time period to see if it's indeed something they want to research more fully.
• DIY Guides for Analytical Writing Assignments

• Types of Assignments
• Unpacking the Elements of Writing Prompts
• Formative Writing Assignments
• Single-Source Analysis
• Research Essays
• Multi-Modal or Creative Projects
• Giving Feedback to Students

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Home » Blog » A Step-by-Step Guide to Writing a Comparative Analysis

A Step-by-Step Guide to Writing a Comparative Analysis

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How to Write a Comparative Analysis with Examples

Writing a comparative analysis in a research paper is not as difficult as many people might tend to think. With some tips, it is possible to write an outstanding comparative review. There are steps that must be utilized to attain this result. They are as detailed in this article.

Within the literary, academic, and journalistic world, analysis allows exposing ideas and arguments in front of a context, making it an important material for discussion within professional work.

Within this genre, we can find a comparative analysis. For some authors, the comparative essay is defined as the text where two opposing positions are proposed or where two theses are verified. The author intends to make the reader reflect on a specific topic through this comparison. It consists of giving a written opinion about two positions, which are compared between them to conclude. Do you know how to write a comparative essay? In this article, we will explain how to do it step by step.

So, let’s see the guidelines you must follow to achieve a good comparative analysis.

How to Write a Good Comparative Analysis

The structure.

The approach is generally developed in the first paragraph or at the beginning of the work. Its objective is to propose the author’s position regarding a specific subject. Generally, this approach specifies the objective to be achieved. You must be clear about what topic you will deal with, what you want to explain, and what perspectives will be used in your comparative analysis, and you must also define who you write for.

As it is a comparative text, it begins with a general observation that can serve as a context for both approaches, then begins by establishing the arguments in each of the two cases. Do not forget to compare both objects of study according to each argument or idea to develop.

Let it be the reader himself who finds or defines his position in this essay and chooses one of the two alternatives.

In this entry, there are two possibilities of approach: one deductive and the other inductive. The deductive method raises the issue, and you use your analysis of the variables to guide the reader to draw their conclusions or fix a position on the issue. While the inductive method starts with an argument, developing each variable until the topic’s approach or problem is reached. The two ways of approaching the subject are viable. Choose the one that is easiest for you to work with.

At the end of this section, your audience should:

• First, clearly understand what topics you will cover in your essay, what you want to explain, and under what positions or perspectives you will do it. It begins with a general observation that establishes the similarity between the two subjects and then moves the essay’s focus to the concrete.
• The reader should understand which points will be examined and which will not be examined in the comparison. At the end of the introduction, state your preference, or describe the two subjects’ meaning.
• Your readers should be able to describe the ideas you will treat. Make a detailed exposition of its characteristics, history, consequences, and development that you consider appropriate. Your comparative analysis should expose the characteristics of the second position on which you want to speak as much as in the first one.

Development of Body

Generally, in the body of the essay, the author presents all the arguments that support his thesis, which gives him a reflective and justifying body of the author’s initial statement. Depending on the length of the work, which can range from two to 15 pages, each paragraph or before a title corresponds to an argument’s development.

After speaking on the subject, the author must close the essay, conclude, show the findings of his work, and/or show the conclusions he reached. You must write a final closing paragraph as a conclusion, exposing a confrontation between the two positions. Try to create a fight between them so that the reader gets involved. The conclusion should give a brief and general summary of the most important similarities and differences. It should end with a personal statement, an opinion, and the “what then?” – what is important about the two things being compared.

Readers should be left feeling that this essay’s different threads have been put together coherently, that they have learned something – and they must be sure that this is the end – that they do not look around for missing pages. And finally, your assessment must explain your solidarity position and why you prefer it to the other.

Examples of How to Write a Comparative Analysis

Comparative analysis example 1:.

Paragraph 1: Messi’s preferred position / Ronaldo’s preferred position.

Paragraph 2: Messi’s play style / Ronaldo’s play style.

Paragraph 3: Messi aerial game / Ronaldo aerial game.

Comparative Analysis Example 2:

Paragraph 1: Messi teamwork.

Paragraph 2: Ronaldo’s teamwork.

Paragraph 3: Messi stopped the ball.

Paragraph 4: Ronaldo’s stopped the ball.

Paragraph 5: Messi’s achievements.

Paragraph 6: Ronaldo’s achievements.

Few Important Rules for Comparative analysis

Even if the exercise sounds simple, a few rules should be followed to help your audience as best as possible make the best decision.

1. Clearly state your position

The first question is, “Why are you doing a comparison analysis”? To highlight your view or ideas over another, or simply to compare two (or more) solutions that do not belong to you? You must clearly state your position to your reader, and so does your credibility.

Be honest and state, for example:

• The idea you are trying to espouse
• The framework you are using
• The reason why you are doing this comparison is the objective

In addition to the above, you must be consistent with the exposition of your ideas.

2. Stay objective

Even if you include your personal ideology in your comparison, stay objective. Your readers will not appreciate it when you point out all the disadvantages of one idea while you display the advantages of the other. Your comparison will turn into advertising. You have to raise weak points and strong points on both sides.

These analyses are always subjective, so you must clarify which position convinces you the most.

3. Think about audience’s expectations

The research paper is intended for your readers, meaning you must consider their expectations when writing your review. Put aside your desire to sell your desired idea and take your readers’ perspective:

• What information are they interested in?
• What are their criteria?
• What do they want to know?
• What do they want from the product or service?

Again, it is about being objective in all your statements.

4. Organize information

It is important to structure your comments for your readers to want to read your comparative analysis. The idea is to make it easy for your readers to navigate your paper and get them to find the information that interests them quickly.

5. End with a conclusion

You’ve tried to be as objective as possible throughout your comparison, and now is the time to let go, as we have mentioned many times in this post. In your conclusion, you can go directly to your readers and give your opinion. With a few tips, you can also encourage them to go towards one or the other idea.

Note: If time is not an issue, the best way to review the essay is to leave it for one day. Go for a walk, eat something, have fun, and forget. Then it’s time to return to the text, find and fix problems. This must be done separately; first, find all the problems you can without correcting them. Although doing it simultaneously is tempting, it is smarter to do it separately. It is effective and fast.

Tips on Comparative Analysis

Be concise or accurate in your analysis and dissertation of the topic.

Sometimes the authors believe that the more elaborate the language and the more extensive the writing, the better the writers or essayists. On the contrary, a good essay refers to an exact topic analysis, where the reader can dynamically advance the work and understand the author’s position.

Use only the arguments necessary to explain the topic, do not talk too much. You risk being redundant or repetitive, making the text-heavy when reading and understanding it.

Write in Short Sentences

Just as we recommend that you do not redound in your texts, we also encourage you to write with short sentences. They give dynamism to the text. Communication is direct. The reader advances in the text and understands much more.

Include Reflections in Your Text

Supporting your approach with reflections or quotes from authors makes your essay more important. Above all, use those arguments that justify or strengthen your position regarding one thesis or the other.

Text Revision

Since comparative analysis can tend to be a subjective work, you must let it “sit” for a day or a few hours and read it again. This exercise will allow you to make corrections. Modify those aspects that are not clear enough for you. And you can improve it in a few words. Once you do this exercise, you can submit it just like this.

If you like this article, see others like it:

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• v.4(2); 2014 Jun

Using qualitative comparative analysis to understand and quantify translation and implementation

Heather kane.

RTI International, 3040 Cornwallis Road, Research Triangle Park, P.O. Box 12194, Durham, NC 27709 USA

Megan A Lewis

Pamela a williams, leila c kahwati.

Understanding the factors that facilitate implementation of behavioral medicine programs into practice can advance translational science. Often, translation or implementation studies use case study methods with small sample sizes. Methodological approaches that systematize findings from these types of studies are needed to improve rigor and advance the field. Qualitative comparative analysis (QCA) is a method and analytical approach that can advance implementation science. QCA offers an approach for rigorously conducting translational and implementation research limited by a small number of cases. We describe the methodological and analytic approach for using QCA and provide examples of its use in the health and health services literature. QCA brings together qualitative or quantitative data derived from cases to identify necessary and sufficient conditions for an outcome. QCA offers advantages for researchers interested in analyzing complex programs and for practitioners interested in developing programs that achieve successful health outcomes.

INTRODUCTION

In this paper, we describe the methodological features and advantages of using qualitative comparative analysis (QCA). QCA is sometimes called a “mixed method.” It refers to both a specific research approach and an analytic technique that is distinct from and offers several advantages over traditional qualitative and quantitative methods [ 1 – 4 ]. It can be used to (1) analyze small to medium numbers of cases (e.g., 10 to 50) when traditional statistical methods are not possible, (2) examine complex combinations of explanatory factors associated with translation or implementation “success,” and (3) combine qualitative and quantitative data using a unified and systematic analytic approach.

This method may be especially pertinent for behavioral medicine given the growing interest in implementation science [ 5 ]. Translating behavioral medicine research and interventions into useful practice and policy requires an understanding of the implementation context. Understanding the context under which interventions work and how different ways of implementing an intervention lead to successful outcomes are required for “T3” (i.e., dissemination and implementation of evidence-based interventions) and “T4” translations (i.e., policy development to encourage evidence-based intervention use among various stakeholders) [ 6 , 7 ].

Case studies are a common way to assess different program implementation approaches and to examine complex systems (e.g., health care delivery systems, interventions in community settings) [ 8 ]. However, multiple case studies often have small, naturally limited samples or populations; small samples and populations lack adequate power to support conventional, statistical analyses. Case studies also may use mixed-method approaches, but typically when researchers collect quantitative and qualitative data in tandem, they rarely integrate both types of data systematically in the analysis. QCA offers solutions for the challenges posed by case studies and provides a useful analytic tool for translating research into policy recommendations. Using QCA methods could aid behavioral medicine researchers who seek to translate research from randomized controlled trials into practice settings to understand implementation. In this paper, we describe the conceptual basis of QCA, its application in the health and health services literature, and its features and limitations.

CONCEPTUAL BASIS OF QCA

QCA has its foundations in historical, comparative social science. Researchers in this field developed QCA because probabilistic methods failed to capture the complexity of social phenomena and required large sample sizes [ 1 ]. Recently, this method has made inroads into health research and evaluation [ 9 – 13 ] because of several useful features as follows: (1) it models equifinality , which is the ability to identify more than one causal pathway to an outcome (or absence of the outcome); (2) it identifies conjunctural causation , which means that single conditions may not display their effects on their own, but only in conjunction with other conditions; and (3) it implies asymmetrical relationships between causal conditions and outcomes, which means that causal pathways for achieving the outcome differ from causal pathways for failing to achieve the outcome.

QCA is a case-oriented approach that examines relationships between conditions (similar to explanatory variables in regression models) and an outcome using set theory; a branch of mathematics or of symbolic logic that deals with the nature and relations of sets. A set-theoretic approach to modeling causality differs from probabilistic methods, which examines the independent, additive influence of variables on an outcome. Regression models, based on underlying assumptions about sampling and distribution of the data, ask “what factor, holding all other factors constant at each factor’s average, will increase (or decrease) the likelihood of an outcome .” QCA, an approach based on the examination of set, subset, and superset relationships, asks “ what conditions —alone or in combination with other conditions—are necessary or sufficient to produce an outcome .” For additional QCA definitions, see Ragin [ 4 ].

Necessary conditions are those that exhibit a superset relationship with the outcome set and are conditions or combinations of conditions that must be present for an outcome to occur. In assessing necessity, a researcher “identifies conditions shared by cases with the same outcome” [ 4 ] (p. 20). Figure  1 shows a hypothetical example. In this figure, condition X is a necessary condition for an effective intervention because all cases with condition X are also members of the set of cases with the outcome present; however, condition X is not sufficient for an effective intervention because it is possible to be a member of the set of cases with condition X, but not be a member of the outcome set [ 14 ].

Necessary and sufficient conditions and set-theoretic relationships

Sufficient conditions exhibit subset relationships with an outcome set and demonstrate that “the cause in question produces the outcome in question” [ 3 ] (p. 92). Figure  1 shows the multiple and different combinations of conditions that produce the hypothetical outcome, “effective intervention,” (1) by having condition A present, (2) by having condition D present, or (3) by having the combination of conditions B and C present. None of these conditions is necessary and any one of these conditions or combinations of conditions is sufficient for the outcome of an effective intervention.

QCA AS AN APPROACH AND AS AN ANALYTIC TECHNIQUE

The term “QCA” is sometimes used to refer to the comparative research approach but also refers to the “analytic moment” during which Boolean algebra and set theory logic is applied to truth tables constructed from data derived from included cases. Figure  2 characterizes this distinction. Although this figure depicts steps as sequential, like many research endeavors, these steps are somewhat iterative, with respecification and reanalysis occurring along the way to final findings. We describe each of the essential steps of QCA as an approach and analytic technique and provide examples of how it has been used in health-related research.

QCA as an approach and as an analytic technique

Operationalizing the research question

Like other types of studies, the first step involves identifying the research question(s) and developing a conceptual model. This step guides the study as a whole and also informs case, condition (c.f., variable), and outcome selection. As mentioned above, QCA frames research questions differently than traditional quantitative or qualitative methods. Research questions appropriate for a QCA approach would seek to identify the necessary and sufficient conditions required to achieve the outcome. Thus, formulating a QCA research question emphasizes what program components or features—individually or in combination—need to be in place for a program or intervention to have a chance at being effective (i.e., necessary conditions) and what program components or features—individually or in combination—would produce the outcome (i.e., sufficient conditions). For example, a set theoretic hypothesis would be as follows: If a program is supported by strong organizational capacity and a comprehensive planning process, then the program will be successful. A hypothesis better addressed by probabilistic methods would be as follows: Organizational capacity, holding all other factors constant, increases the likelihood that a program will be successful.

For example, Longest and Thoits [ 15 ] drew on an extant stress process model to assess whether the pathways leading to psychological distress differed for women and men. Using QCA was appropriate for their study because the stress process model “suggests that particular patterns of predictors experienced in tandem may have unique relationships with health outcomes” (p. 4, italics added). They theorized that predictors would exhibit effects in combination because some aspects of the stress process model would buffer the risk of distress (e.g., social support) while others simultaneously would increase the risk (e.g., negative life events).

Identify cases

The number of cases in a QCA analysis may be determined by the population (e.g., 10 intervention sites, 30 grantees). When particular cases can be chosen from a larger population, Berg-Schlosser and De Meur [ 16 ] offer other strategies and best practices for choosing cases. Unless the number of cases relies on an existing population (i.e., 30 programs or grantees), the outcome of interest and existing theory drive case selection, unlike variable-oriented research [ 3 , 4 ] in which numbers are driven by statistical power considerations and depend on variation in the dependent variable. For use in causal inference, both cases that exhibit and do not exhibit the outcome should be included [ 16 ]. If a researcher is interested in developing typologies or concept formation, he or she may wish to examine similar cases that exhibit differences on the outcome or to explore cases that exhibit the same outcome [ 14 , 16 ].

For example, Kahwati et al. [ 9 ] examined the structure, policies, and processes that might lead to an effective clinical weight management program in a large national integrated health care system, as measured by mean weight loss among patients treated at the facility. To examine pathways that lead to both better and poorer facility-level weight loss, 11 facilities from among those with the largest weight loss outcomes and 11 facilities from among those with the smallest were included. By choosing cases based on specific outcomes, Kahwati et al. could identify multiple patterns of success (or failure) that explain the outcome rather than the variability associated with the outcome.

Identify conditions and outcome sets

Selecting conditions relies on the research question, conceptual model, and number of cases similar to other research methods. Conditions (or “sets” or “condition sets”) refer to the explanatory factors in a model; they are similar to variables. Because QCA research questions assess necessary and sufficient conditions, a researcher should consider which conditions in the conceptual model would theoretically produce the outcome individually or in combination. This helps to focus the analysis and number of conditions. Ideally, for a case study design with a small (e.g., 10–15) or intermediate (e.g., 16–100) number of cases, one should aim for fewer than five conditions because in QCA a researcher assesses all possible configurations of conditions. Adding conditions to the model increases the possible number of combinations exponentially (i.e., 2 k , where k = the number of conditions). For three conditions, eight possible combinations of the selected conditions exist as follows: the presence of A, B, C together, the lack of A with B and C present, the lack of A and lack of B with C present, and so forth. Having too many conditions will likely mean that no cases fall into a particular configuration, and that configuration cannot be assessed by empirical examples. When one or more configurations are not represented by the cases, this is known as limited diversity, and QCA experts suggest multiple strategies for managing such situations [ 4 , 14 ].

For example, Ford et al. [ 10 ] studied health departments’ implementation of core public health functions and organizational factors (e.g., resource availability, adaptability) and how those conditions lead to superior and inferior population health changes. They operationalized three core public functions (i.e., assessment of environmental and population public health needs, capacity for policy development, and authority over assurance of healthcare operations) and operationalized those for their study by using composite measures of varied health indicators compiled in a UnitedHealth Group report. In this examination of 41 state health departments, the authors found that all three core public health functions were necessary for population health improvement. The absence of any of the core public health functions was sufficient for poorer population health outcomes; thus, only the health departments with the ability to perform all three core functions had improved outcomes. Additionally, these three core functions in combination with either resource availability or adaptability were sufficient combinations (i.e., causal pathways) for improved population health outcomes.

Calibrate condition and outcome sets

Calibration refers to “adjusting (measures) so that they match or conform to dependably known standards” and is a common way of standardizing data in the physical sciences [ 4 ] (p. 72). Calibration requires the researcher to make sense of variation in the data and apply expert knowledge about what aspects of the variation are meaningful. Because calibration depends on defining conditions based on those “dependably known standards,” QCA relies on expert substantive knowledge, theory, or criteria external to the data themselves [ 14 ]. This may require researchers to collaborate closely with program implementers.

In QCA, one can use “crisp” set or “fuzzy” set calibration. Crisp sets, which are similar to dichotomous categorical variables in regression, establish decision rules defining a case as fully in the set (i.e., condition) or fully out of the set; fuzzy sets establish degrees of membership in a set. Fuzzy sets “differentiate between different levels of belonging anchored by two extreme membership scores at 1 and 0” [ 14 ] (p.28). They can be continuous (0, 0.1, 0.2,..) or have qualitatively defined anchor points (e.g., 0 is fully out of the set; 0.33 is more out than in the set; 0.66 is more in than out of the set; 1 is fully in the set). A researcher selects fuzzy sets and the corresponding resolution (i.e., continuous, four cutoff points, six cutoff) based on theory and meaningful differences between cases and must be able to provide a verbal description for each cutoff point [ 14 ]. If, for example, a researcher cannot distinguish between 0.7 and 0.8 membership in a set, then a more continuous scoring of cases would not be useful, rather a four point cutoff may better characterize the data. Although crisp and fuzzy sets are more commonly used, new multivariate forms of QCA are emerging as are variants that incorporate elements of time [ 14 , 17 , 18 ].

Fuzzy sets have the advantage of maintaining more detail for data with continuous values. However, this strength also makes interpretation more difficult. When an observation is coded with fuzzy sets, a particular observation has some degree of membership in the set “condition A” and in the set “condition NOT A.” Thus, when doing analyses to identify sufficient conditions, a researcher must make a judgment call on what benchmark constitutes recommendation threshold for policy or programmatic action.

In creating decision rules for calibration, a researcher can use a variety of techniques to identify cutoff points or anchors. For qualitative conditions, a researcher can define decision rules by drawing from the literature and knowledge of the intervention context. For conditions with numeric values, a researcher can also employ statistical approaches. Ideally, when using statistical approaches, a researcher should establish thresholds using substantive knowledge about set membership (thus, translating variation into meaningful categories). Although measures of central tendency (e.g., cases with a value above the median are considered fully in the set) can be used to set cutoff points, some experts consider the sole use of this method to be flawed because case classification is determined by a case’s relative value in regard to other cases as opposed to its absolute value in reference to an external referent [ 14 ].

For example, in their study of National Cancer Institutes’ Community Clinical Oncology Program (NCI CCOP), Weiner et al. [ 19 ] had numeric data on their five study measures. They transformed their study measures by using their knowledge of the CCOP and by asking NCI officials to identify three values: full membership in a set, a point of maximum ambiguity, and nonmembership in the set. For their outcome set, high accrual in clinical trials, they established 100 patients enrolled accrual as fully in the set of high accrual, 70 as a point of ambiguity (neither in nor out of the set), and 50 and below as fully out of the set because “CCOPs must maintain a minimum of 50 patients to maintain CCOP funding” (p. 288). By using QCA and operationalizing condition sets in this way, they were able to answer what condition sets produce high accrual, not what factors predict more accrual. The advantage is that by using this approach and analytic technique, they were able to identify sets of factors that are linked with a very specific outcome of interest.

Obtain primary or secondary data

Data sources vary based on the study, availability of the data, and feasibility of data collection; data can be qualitative or quantitative, a feature useful for mixed-methods studies and systematically integrating these different types of data is a major strength of this approach. Qualitative data include program documents and descriptions, key informant interviews, and archival data (e.g., program documents, records, policies); quantitative data consists of surveys, surveillance or registry data, and electronic health records.

For instance, Schensul et al. [ 20 ] relied on in-depth interviews for their analysis; Chuang et al. [ 21 ] and Longest and Thoits [ 15 ] drew on survey data for theirs. Kahwati et al. [ 9 ] used a mixed-method approach combining data from key informant interviews, program documents, and electronic health records. Any type of data can be used to inform the calibration of conditions.

Assign set membership scores

Assigning set membership scores involves applying the decision rules that were established during the calibration phase. To accomplish this, the research team should then use the extracted data for each case, apply the decision rule for the condition, and discuss discrepancies in the data sources. In their study of factors that influence health care policy development in Florida, Harkreader and Imershein [ 22 ] coded contextual factors that supported state involvement in the health care market. Drawing on a review of archival data and using crisp set coding, they assigned a value of 1 for the presence of a contextual factor (e.g., presence of federal financial incentives promoting policy, unified health care provider policy position in opposition to state policy, state agency supporting policy position) and 0 for the absence of a contextual factor.

Construct truth table

After completing the coding, researchers create a “truth table” for analysis. A truth table lists all of the possible configurations of conditions, the number of cases that fall into that configuration, and the “consistency” of the cases. Consistency quantifies the extent to which cases that share similar conditions exhibit the same outcome; in crisp sets, the consistency value is the proportion of cases that exhibit the outcome. Fuzzy sets require a different calculation to establish consistency and are described at length in other sources [ 1 – 4 , 14 ]. Table  1 displays a hypothetical truth table for three conditions using crisp sets.

Sample of a hypothetical truth table for crisp sets

1 fully in the set, 0 fully out of the set

QCA AS AN ANALYTIC TECHNIQUE

The research steps to this point fall into QCA as an approach to understanding social and health phenomena. Analysis of the truth table is the sine qua non of QCA as an analytic technique. In this section, we provide an overview of the analysis process, but analytic techniques and emerging forms of analysis are described in multiple texts [ 3 , 4 , 14 , 17 ]. The use of computer software to conduct truth table analysis is recommended and several software options are available including Stata, fsQCA, Tosmana, and R.

A truth table analysis first involves the researcher assessing which (if any) conditions are individually necessary or sufficient for achieving the outcome, and then second, examining whether any configurations of conditions are necessary or sufficient. In instances where contradictions in outcomes from the same configuration pattern occur (i.e., one case from a configuration has the outcome; one does not), the researcher should also consider whether the model is properly specified and conditions are calibrated accurately. Thus, this stage of the analysis may reveal the need to review how conditions are defined and whether the definition should be recalibrated. Similar to qualitative and quantitative research approaches, analysis is iterative.

Additionally, the researcher examines the truth table to assess whether all logically possible configurations have empiric cases. As described above, when configurations lack cases, the problem of limited diversity occurs. Configurations without representative cases are known as logical remainders, and the researcher must consider how to deal with those. The analysis of logical remainders depends on the particular theory guiding the research and the research priorities. How a researcher manages the logical remainders has implications for the final solution, but none of the solutions based on the truth table will contradict the empirical evidence [ 14 ]. To generate the most conservative solution term, a researcher makes no assumptions about truth table rows with no cases (or very few cases in larger N studies) and excludes them from the logical minimization process. Alternately, a researcher can choose to include (or exclude) rows with no cases from analysis, which would generate a solution that is a superset of the conservative solution. Choosing inclusion criteria for logical remainders also depends on theory and what may be empirically possible. For example, in studying governments, it would be unlikely to have a case that is a democracy (“condition A”), but has a dictator (“condition B”). In that circumstance, the researcher may choose to exclude that theoretically implausible row from the logical minimization process.

Third, once all the solutions have been identified, the researcher mathematically reduces the solution [ 1 , 14 ]. For example, if the list of solutions contains two identical configurations, except that in one configuration A is absent and in the other A is present, then A can be dropped from those two solutions. Finally, the researcher computes two parameters of fit: coverage and consistency. Coverage determines the empirical relevance of a solution and quantifies the variation in causal pathways to an outcome [ 14 ]. When coverage of a causal pathway is high, the more common the solution is, and more of the outcome is accounted for by the pathway. However, maximum coverage may be less critical in implementation research because understanding all of the pathways to success may be as helpful as understanding the most common pathway. Consistency assesses whether the causal pathway produces the outcome regularly (“the degree to which the empirical data are in line with a postulated subset relation,” p. 324 [ 14 ]); a high consistency value (e.g., 1.00 or 100 %) would indicate that all cases in a causal pathway produced the outcome. A low consistency value would suggest that a particular pathway was not successful in producing the outcome on a regular basis, and thus, for translational purposes, should not be recommended for policy or practice changes. A causal pathway with high consistency and coverage values indicates a result useful for providing guidance; a high consistency with a lower coverage score also has value in showing a causal pathway that successfully produced the outcome, but did so less frequently.

For example, Kahwati et al. [ 9 ] examined their truth table and analyzed the data for single conditions and combinations of conditions that were necessary for higher or lower facility-level patient weight loss outcomes. The truth table analysis revealed two necessary conditions and four sufficient combinations of conditions. Because of significant challenges with logical remainders, they used a bottom-up approach to assess whether combinations of conditions yielded the outcome. This entailed pairing conditions to ensure parsimony and maximize coverage. With a smaller number of conditions, a researcher could hypothetically find that more cases share similar characteristics and could assess whether those cases exhibit the same outcome of interest.

At the completion of the truth table analysis, Kahwati et al. [ 9 ] used the qualitative data from site interviews to provide rich examples to illustrate the QCA solutions that were identified, which explained what the solutions meant in clinical practice for weight management. For example, having an involved champion (usually a physician), in combination with low facility accountability, was sufficient for program success (i.e., better weight loss outcomes) and was related to better facility weight loss. In reviewing the qualitative data, Kahwati et al. [ 9 ] discovered that involved champions integrate program activities into their clinical routines and discuss issues as they arise with other program staff. Because involved champions and other program staff communicated informally on a regular basis, formal accountability structures were less of a priority.

ADVANTAGES AND LIMITATIONS OF QCA

Because translational (and other health-related) researchers may be interested in which intervention features—alone or in combination—achieve distinct outcomes (e.g., achievement of program outcomes, reduction in health disparities), QCA is well suited for translational research. To assess combinations of variables in regression, a researcher relies on interaction effects, which, although useful, become difficult to interpret when three, four, or more variables are combined. Furthermore, in regression and other variable-oriented approaches, independent variables are held constant at the average across the study population to isolate the independent effect of that variable, but this masks how factors may interact with each other in ways that impact the ultimate outcomes. In translational research, context matters and QCA treats each case holistically, allowing each case to keep its own values for each condition.

Multiple case studies or studies with the organization as the unit of analysis often involve a small or intermediate number of cases. This hinders the use of standard statistical analyses; researchers are less likely to find statistical significance with small sample sizes. However, QCA draws on analyses of set relations to support small-N studies and to identify the conditions or combinations of conditions that are necessary or sufficient for an outcome of interest and may yield results when probabilistic methods cannot.

Finally, QCA is based on an asymmetric concept of causation , which means that the absence of a sufficient condition associated with an outcome does not necessarily describe the causal pathway to the absence of the outcome [ 14 ]. These characteristics can be helpful for translational researchers who are trying to study or implement complex interventions, where more than one way to implement a program might be effective and where studying both effective and ineffective implementation practices can yield useful information.

QCA has several limitations that researchers should consider before choosing it as a potential methodological approach. With small- and intermediate-N studies, QCA must be theory-driven and circumscribed by priority questions. That is, a researcher ideally should not use a “kitchen sink” approach to test every conceivable condition or combination of conditions because the number of combinations increases exponentially with the addition of another condition. With a small number of cases and too many conditions, the sample would not have enough cases to provide examples of all the possible configurations of conditions (i.e., limited diversity), or the analysis would be constrained to describing the characteristics of the cases, which would have less value than determining whether some conditions or some combination of conditions led to actual program success. However, if the number of conditions cannot be reduced, alternate QCA techniques, such as a bottom-up approach to QCA or two-step QCA, can be used [ 14 ].

Another limitation is that programs or clinical interventions involved in a cross-site analysis may have unique programs that do not seem comparable. Cases must share some degree of comparability to use QCA [ 16 ]. Researchers can manage this challenge by taking a broader view of the program(s) and comparing them on broader characteristics or concepts, such as high/low organizational capacity, established partnerships, and program planning, if these would provide meaningful conclusions. Taking this approach will require careful definition of each of these concepts within the context of a particular initiative. Definitions may also need to be revised as the data are gathered and calibration begins.

Finally, as mentioned above, crisp set calibration dichotomizes conditions of interest; this form of calibration means that in some cases, the finer grained differences and precision in a condition may be lost [ 3 ]. Crisp set calibration provides more easily interpretable and actionable results and is appropriate if researchers are primarily interested in the presence or absence of a particular program feature or organizational characteristic to understand translation or implementation.

QCA offers an additional methodological approach for researchers to conduct rigorous comparative analyses while drawing on the rich, detailed data collected as part of a case study. However, as Rihoux, Benoit, and Ragin [ 17 ] note, QCA is not a miracle method, nor a panacea for all studies that use case study methods. Furthermore, it may not always be the most suitable approach for certain types of translational and implementation research. We outlined the multiple steps needed to conduct a comprehensive QCA. QCA is a good approach for the examination of causal complexity, and equifinality could be helpful to behavioral medicine researchers who seek to translate evidence-based interventions in real-world settings. In reality, multiple program models can lead to success, and this method accommodates a more complex and varied understanding of these patterns and factors.

Implications

Practice : Identifying multiple successful intervention models (equifinality) can aid in selecting a practice model relevant to a context, and can facilitate implementation.

Policy : QCA can be used to develop actionable policy information for decision makers that accommodates contextual factors.

Research : Researchers can use QCA to understand causal complexity in translational or implementation research and to assess the relationships between policies, interventions, or procedures and successful outcomes.

EducationalWave

Pros and Cons of Comparative Research

Comparative research, widely recognized for its ability to illuminate differences and similarities across various contexts, stands as a cornerstone in the advancement of knowledge across disciplines. By juxtaposing disparate entities, be they societies, economies, or policies, it unveils patterns and dynamics that might remain obscured in isolated analyses.

Yet, this methodological approach is not without its critiques, primarily concerning its susceptibility to oversimplification and the potential misapplication of findings across diverse contexts. The ensuing debate on the merits and limitations of comparative research invites a nuanced examination of its methodological underpinnings and implications for future scholarly inquiry.

Table of Contents

Key Takeaways

• Comparative research enhances decision-making by identifying best practices and areas for improvement.
• It broadens perspectives and fosters cross-cultural understanding through the examination of diverse cases.
• Cultural and methodological biases in comparative research can lead to misinterpretation and undermine credibility.
• Evolving methodologies aim to address biases and expand the scope, enriching comparative studies with interdisciplinary collaboration.

Understanding Comparative Research

Comparative research, a methodological approach that entails the juxtaposition of different entities to underscore their similarities and differences, plays a pivotal role in enhancing decision-making processes. This research strategy involves a systematic comparison of various products, processes, or systems, aiming to uncover the distinct strengths and weaknesses inherent in each. By doing so, it facilitates a comprehensive understanding of the available options, guiding stakeholders toward more informed choices.

The essence of comparative research lies in its ability to dissect and analyze trends, patterns, and best practices across diverse contexts. This analytical depth not only enriches the knowledge base of the researchers but also contributes significantly to the development of critical thinking and problem-solving skills. The comparative method is particularly valuable in its provision of insights into the effectiveness of different strategies or approaches, thereby enabling decision-makers to select the most suitable options based on empirical evidence.

Moreover, by examining multiple cases or instances side by side, comparative research fosters a holistic view of the subject matter. This broadened perspective is instrumental in identifying viable solutions and innovations that are informed by a thorough evaluation of alternatives, thus leading to strategic and effective decision-making.

Advantages of Comparative Analysis

Comparative analysis offers a multitude of benefits that are instrumental in the strategic planning of businesses. By facilitating an enhanced understanding and providing broader perspectives, it becomes an invaluable tool for identifying competitive advantages and areas for improvement.

This approach not only aids in informed decision-making but also ensures that resources are allocated efficiently for sustainable growth.

Enhanced Understanding

By examining various cases or subjects in parallel, researchers gain a broader perspective and deeper insights into their study area. Comparative research allows for the uncovering of underlying patterns and similarities across different cases, which might remain unnoticed in single-case studies. This methodology not only challenges prevailing assumptions but also fosters critical thinking, thereby enhancing creativity and innovation in the field.

Broader Perspectives

Building on the enhanced understanding that the methodology provides, broader perspectives offered by comparative analysis play a pivotal role in further enriching research outcomes. By examining different cases side by side, this approach not only broadens the researcher’s perspective but also uncovers underlying patterns and similarities that single-case studies may overlook. It challenges prevailing assumptions, fostering critical thinking that paves the way for creativity and innovation.

Moreover, comparing various aspects yields a more nuanced comprehension of the subject’s complexities, enhancing cross-cultural understanding by highlighting both similarities and differences across societies. This fosters a deeper appreciation for diversity, contributing significantly to a more well-rounded and informed research conclusion.

Broadening Perspectives

Exploring diverse cases or subjects side by side, comparative research significantly broadens perspectives. This methodological approach is instrumental in uncovering underlying patterns and similarities that may be obscured in the confines of single-case studies. By juxtaposing different instances, researchers are not only able to recognize commonalities but also to appreciate the unique facets of each case. This duality enhances the depth of understanding surrounding the subject matter, illuminating nuances and complexities that a more myopic lens might overlook.

Moreover, comparative research challenges entrenched assumptions and encourages critical thinking. Presenting contrasting viewpoints compels scholars and practitioners alike to question preconceived notions, fostering a more open-minded approach to inquiry. This intellectual rigor is essential in cultivating a fertile ground for creativity and innovation. Exposure to diverse perspectives and methodologies not only enriches the researcher’s toolkit but also sparks novel ideas and approaches.

Ultimately, the process of comparing and contrasting leads to a more comprehensive and nuanced comprehension of the subject at hand. Through this lens, comparative research proves to be a powerful vehicle for broadening perspectives, pushing the boundaries of conventional wisdom, and advancing knowledge in a myriad of fields.

Cross-Cultural Insights

Moving beyond broadening perspectives, comparative research also offers invaluable insights into the cultural fabric that weaves societies together. By delving into the diverse traditions, norms, and values that distinguish one society from another, this type of research illuminates the intricate mosaic of human cultures. It unravels the unique characteristics, practices, and beliefs that are foundational to each culture, thereby enriching our understanding of the global community.

Comparative research acts as a bridge, fostering an appreciation for the rich tapestry of cultural diversity that exists worldwide. It promotes a spirit of inclusion and respect for differences, which is crucial in today’s interconnected world. Through the exchange of ideas that it facilitates, comparative research encourages cross-cultural collaboration, paving the way for innovative solutions to global challenges.

Moreover, by identifying commonalities among cultures, comparative research contributes to bridging cultural gaps. It underscores the shared human experiences that unite us, promoting mutual understanding and solidarity across borders. This aspect of comparative research is essential for nurturing a sense of global citizenship and cooperation, highlighting its significance in promoting a more harmonious world.

Limitations and Challenges

Despite its numerous benefits, comparative research encounters several limitations and challenges that can impact its effectiveness and reliability. One significant hurdle is the potential for oversimplification of complex phenomena. This stems from the focus on identifying similarities and differences, which can sometimes ignore the nuanced and multifaceted nature of the subjects under study. This simplification can lead to a loss of depth and richness in understanding the phenomena.

Another challenge lies in ensuring data comparability across different contexts and settings. Variations in how data is collected, measured, and interpreted can severely affect the validity of research findings. This is particularly problematic when comparing data from diverse regions or industries where standards and practices may vary widely.

Additionally, the limited availability and quality of data from certain areas or sectors can restrict the scope and generalizability of comparative studies. This limitation not only narrows the research’s applicability but also raises questions about its representativeness and accuracy.

Moreover, bias and subjectivity in selecting and interpreting data can significantly influence the outcomes of comparative research. Researchers must navigate these challenges carefully to maintain the integrity and credibility of their findings.

Cultural and Methodological Biases

Understanding the impact of cultural and methodological biases is fundamental to enhancing the accuracy and integrity of comparative research. Cultural biases can skew researchers’ perspectives, leading to the stereotyping, oversimplification, or misinterpretation of cultural practices. These biases not only distort the understanding of different cultures but also undermine the credibility of research findings. To mitigate such biases, researchers must make conscious efforts to deeply understand and respect the diverse cultural backgrounds involved in their studies. This approach helps in presenting a more accurate and comprehensive view of the cultures being compared.

Methodological biases, on the other hand, arise from variations in research methodologies, sample sizes, or data collection techniques across different cultural settings. These biases can significantly affect the validity and reliability of research outcomes, casting doubts on the accuracy of the conclusions drawn. It is crucial for researchers to recognize and address these methodological issues to ensure the production of rigorous and unbiased comparative research findings. Awareness and acknowledgment of both cultural and methodological biases are essential steps in conducting comparative research that is both respectful of cultural diversity and methodologically sound.

Future Directions in Research

As comparative research continues to evolve, attention is increasingly turning towards the development of emerging research methodologies. These advancements promise to refine and expand the scope of comparative studies, particularly through the benefits of interdisciplinary collaboration.

Such collaborations are poised to enrich the comparative research framework, enabling a more nuanced understanding of complex phenomena across different contexts.

Emerging Research Methodologies

Emerging research methodologies in comparative research are increasingly leveraging mixed methods approaches to pave the way for a more nuanced exploration of complex phenomena. These methodologies focus on blending qualitative and quantitative data to achieve a more comprehensive understanding. The integration of advanced technology plays a crucial role in refining these approaches, enabling more efficient data collection and analysis.

• Integrating qualitative and quantitative data for holistic insights
• Utilizing advancements in technology for efficient data collection and analysis
• Leveraging big data analytics and machine learning algorithms to revolutionize comparative studies

These innovations are setting the stage for future advancements in comparative research, making it possible to tackle increasingly complex questions with greater precision and depth.

Interdisciplinary Collaboration Benefits

Interdisciplinary collaboration in comparative research offers a plethora of innovative solutions by merging expertise from various academic fields. This approach not only facilitates a holistic understanding of complex phenomena by integrating insights from diverse disciplines but also enhances the depth and breadth of analysis in comparative studies.

Such collaboration bridges gaps between disciplines, uncovering unique perspectives and shedding light on different aspects of a research topic. The fusion of varied academic lenses fosters creativity and encourages thinking outside traditional disciplinary boundaries.

Consequently, interdisciplinary teamwork enriches the research process, making it more comprehensive and insightful. This collaborative method positions comparative research at the forefront of innovation, capable of addressing multifaceted questions with enriched, multifocal answers.

In conclusion, comparative research serves as a critical approach for advancing knowledge across various disciplines, facilitating a comprehensive understanding of global phenomena through the lens of cross-cultural insights.

Despite its inherent challenges, such as potential biases and the risk of oversimplification, the systematic and thoughtful application of comparative analysis significantly contributes to the identification of universal patterns and divergent trends.

Therefore, the continuous refinement of methodologies and the careful consideration of contextual nuances are imperative for harnessing the full potential of comparative research in driving forward scholarly inquiry and practical applications.

Related Posts:

• Pros and Cons of Meta Analysis
• Pros and Cons of Narrative Research
• Pros and Cons of Scientific Method

Related posts:

• 20 Pros and Cons of Generac Generators
• Pros and Cons of Stove Under Window
• 20 Pros and Cons of Quantitative Research

Educational Wave Team

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• > The Case for Case Studies
• > Selecting Cases for Comparative Sequential Analysis

Book contents

• The Case for Case Studies
• Strategies for Social Inquiry
• Copyright page
• Contributors
• Preface and Acknowledgments
• 1 Using Case Studies to Enhance the Quality of Explanation and Implementation
• Part I Internal and External Validity Issues in Case Study Research
• Part II Ensuring High-Quality Case Studies
• 6 Descriptive Accuracy in Interview-Based Case Studies
• 7 Selecting Cases for Comparative Sequential Analysis
• 8 The Transparency Revolution in Qualitative Social Science
• Part III Putting Case Studies to Work: Applications to Development Practice

7 - Selecting Cases for Comparative Sequential Analysis

Novel Uses for Old Methods

from Part II - Ensuring High-Quality Case Studies

Published online by Cambridge University Press:  05 May 2022

Pavone analyzes how our evolving understanding of case-based causal inference via process-tracing should alter how we select cases for comparative inquiry. The chapter explicates perhaps the most influential and widely used means to conduct qualitative research involving two or more cases: Mill’s methods of agreement and difference. It then argues that the traditional use of Millian methods of case selection can lead us to treat cases as static units to be synchronically compared rather than as social processes unfolding over time. As a result, Millian methods risk prematurely rejecting and otherwise overlooking (1) ordered causal processes, (2) paced causal processes, and (3) equifinality, or the presence of multiple pathways that produce the same outcome. To address these issues, the chapter develops a set of recommendations to ensure the alignment of Millian methods of case selection with within-case sequential analysis.

7.1 Introduction

In the lead article of the first issue of Comparative politics , Harold Lasswell posited that the “scientific approach” and the “comparative method” are one and the same ( Reference Lasswell Lasswell 1968 : 3). So important is comparative case study research to the modern social sciences that two disciplinary subfields – comparative politics in political science and comparative-historical sociology – crystallized in no small part because of their shared use of comparative case study research ( Reference Collier and Finifter Collier 1993 ; Reference Adams, Clemens, Orloff, Adams, Clemens and Orloff Adams, Clemens, and Orloff 2005 : 22–26; Reference Mahoney and Thelen Mahoney and Thelen 2015 ). As a result, a first-principles methodological debate emerged about the appropriate ways to select cases for causal inquiry. In particular, the diffusion of econometric methods in the social sciences exposed case study researchers to allegations that they were “selecting on the dependent variable” and that “selection bias” would hamper the “answers they get” ( Reference Geddes Geddes 1990 ). Lest they be pushed to randomly select cases or turn to statistical and experimental approaches, case study researchers had to develop a set of persuasive analytic tools for their enterprise.

It is unsurprising, therefore, that there has been a profusion of scholarship discussing case selection over the years. Footnote 1 Reference Gerring and Cojocaru Gerring and Cojocaru (2015) synthesize this literature by deriving no less than five distinct types (representative, anomalous, most-similar, crucial, and most-different) and eighteen subtypes of cases, each with its own logic of case selection. It falls outside the scope of this chapter to provide a descriptive overview of each approach to case selection. Rather, the purpose of the present inquiry is to place the literature on case selection in constructive dialogue with the equally lively and burgeoning body of scholarship on process tracing ( Reference George and Bennett George and Bennett 2005 ; Reference Brady and Collier Brady and Collier 2010 ; Reference Beach and Pedersen Beach and Pedersen 2013 ; Reference Bennett and Checkel Bennett and Checkel 2015 ). I ask a simple question: Should our evolving understanding of causation and our toolkit for case-based causal inference courtesy of process-tracing scholars alter how scholars approach case selection? If so, why, and what may be the most fruitful paths forward?

To propose an answer, this chapter focuses on perhaps the most influential and widely used means to conduct qualitative research involving two or more cases: Mill’s methods of agreement and difference. Also known as the “most-different systems/cases” and “most-similar systems/cases” designs, these strategies have not escaped challenge – although, as we will see, many of these critiques were fallaciously premised on case study research serving as a weaker analogue to econometric analysis. Here, I take a different approach: I argue that the traditional use of Millian methods of case selection can indeed be flawed, but rather because it risks treating cases as static units to be synchronically compared rather than as social processes unfolding over time. As a result, Millian methods risk prematurely rejecting and otherwise overlooking (1) ordered causal processes, (2) paced causal processes, and (3) equifinality, or the presence of multiple pathways that produce the same outcome. While qualitative methodologists have stressed the importance of these processual dynamics, they have been less attentive to how these factors may problematize pairing Millian methods of case selection with within-case process tracing (e.g., Reference Hall, Mahoney and Rueschemeyer Hall 2003 ; Reference Tarrow Tarrow 2010 ; Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 ). This chapter begins to fill that gap.

Taking a more constructive and prescriptive turn, the chapter provides a set of recommendations for ensuring the alignment of Millian methods of case selection with within-case sequential analysis. It begins by outlining how the deductive use of processualist theories can help reformulate Millian case selection designs to accommodate ordered and paced processes (but not equifinal processes). More originally, the chapter concludes by proposing a new, alternative approach to comparative case study research: the method of inductive case selection . By making use of Millian methods to select cases for comparison after a causal process has been identified within a particular case, the method of inductive case selection enables researchers to assess (1) the generalizability of the causal sequences, (2) the logics of scope conditions on the causal argument, and (3) the presence of equifinal pathways to the same outcome. In so doing, scholars can convert the weaknesses of Millian approaches into strengths and better align comparative case study research with the advances of processualist researchers.

Organizationally, the chapter proceeds as follows. Section 7.2 provides an overview of Millian methods for case selection and articulates how the literature on process tracing fits within debates about the utility and shortcomings of the comparative method. Section 7.3 articulates why the traditional use of Millian methods risks blinding the researcher to ordered, paced, and equifinal causal processes, and describes how deductive, processualist theorizing helps attenuate some of these risks. Section 7.4 develops a new inductive method of case selection and provides a number of concrete examples from development practice to illustrate how it can be used by scholars and policy practitioners alike. Section 7.5 concludes.

7.2 Case Selection in Comparative Research

7.2.1 case selection before the processual turn.

Before “process tracing” entered the lexicon of social scientists, the dominant case selection strategy in case study research sought to maximize causal leverage via comparison, particularly via the “methods of agreement and difference” of John Stuart Reference Mill Mill (1843 [1974] : 388–391).

In Mill’s method of difference, the researcher purposively chooses two (or more) cases that experience different outcomes, despite otherwise being very similar on a number of relevant dimensions. Put differently, the researcher seeks to maximize variation in the outcome variable while minimizing variation amongst a set of plausible explanatory variables. It is for this reason that the approach also came to be referred to as the ‘most-similar systems’ or ‘most-similar cases’ design – while Mill’s nomenclature highlights variation in the outcome of interest, the alternative terminology highlights minimal variation amongst a set of possible explanatory factors. The underlying logic of this case selection strategy is that because the cases are so similar, the researcher can subsequently probe for the explanatory factor that actually does exhibit cross-case variation and isolate it as a likely cause.

Mill’s method of agreement is the mirror image of the method of difference. Here, the researcher chooses two (or more) cases that experience similar outcomes despite being very different on a number of relevant dimensions. That is, the researcher seeks to minimize variation in the outcome variable while maximizing variation amongst a set of plausible explanatory variables. An alternative, independent variable-focused terminology for this approach was developed – the ‘most-different systems’ or ‘most-different cases’ design – breeding some confusion. The underlying logic of this case selection strategy is that it helps the researcher isolate the explanatory factor that is similar across the otherwise different cases as a likely cause. Footnote 2

Figure 7.1 Case selection setup under Mill’s methods of difference and agreement

Mill himself did not believe that such methods could yield causal inferences outside of the physical sciences ( Reference Mill Mill 1843 [1974] : 452). Nevertheless, in the 1970s a number of comparative social scientists endorsed Millian methods as the cornerstones of the comparative method. For example, Reference Przeworski and Teune Przeworski and Teune (1970) advocated in favor of the most-different cases design, whereas Reference Lijphart Lijphart (1971) favored the most-similar cases approach. In so doing, scholars sought case selection techniques that would be as analogous as possible to regression analysis: focused on controlling for independent variables across cases, maximizing covariation between the outcome and a plausible explanatory variable, and treating cases as a qualitative equivalent to a row of dataset observations. It is not difficult to see why this contributed to the view that case study research serves as the “inherently flawed” version of econometrics ( Reference Adams, Clemens, Orloff, Adams, Clemens and Orloff Adams, Clemens, and Orloff 2005 : 25; Reference Tarrow Tarrow 2010 ). Indeed, despite his prominence as a case study researcher, Reference Lijphart Lijphart (1975 : 165; Reference Lijphart 1971 : 685) concluded that “because the comparative method must be considered the weaker method,” then “if at all possible one should generally use the statistical (or perhaps even the experimental) method instead.” As Reference Hall, Mahoney and Rueschemeyer Hall (2003 : 380; 396) brilliantly notes, case study research

was deeply influenced by [Lijphart’s] framing of it … [where] the only important observations to be drawn from the cases are taken on the values of the dependent variable and a few explanatory variables … From this perspective, because the number of pertinent observations available from small-N comparison is seriously limited, the analyst lacks the degrees of freedom to consider more than a few explanatory variables, and the value of small-N comparison for causal inference seems distinctly limited.

In other words, the predominant case selection approach through the 1990s sought to do its best to reproduce a regression framework in a small-N setting – hence Lijphart’s concern with the “many variables, small number of cases” problem, which he argued could only be partially mitigated if, inter alia , the researcher increases the number of cases and decreases the number of variables across said cases ( Reference Lijphart 1971 : 685–686). Later works embraced Lijphart’s formulation of the problem even as they sought to address it: for example, Reference Eckstein, Greenstein and Polsby Eckstein (1975 : 85) argued that a “case” could actually be comprised of many “cases” if the unit of analysis shifted from being, say, the electoral system to, say, the voter. Predictably, such interventions invited retorts: Reference Lieberson Lieberson (1994) , for example, claimed that Millian methods’ inability to accommodate probabilistic causation, Footnote 3 interaction effects, and multivariate analysis would remain fatal flaws.

7.2.2 Enter Process Tracing

It is in this light that ‘process tracing’ – a term first used by Reference Hobarth Hobarth (1972) but popularized by Reference George and Lauren George (1979 ) and particularly Reference George and Bennett George and Bennett (2005) , Reference Brady and Collier Brady and Collier (2010) , Reference Beach and Pedersen Beach and Pedersen (2013) , and Reference Bennett and Checkel Bennett and Checkel (2015) – proved revolutionary for the ways in which social scientists conceive of case study research. Cases have gradually been reconceptualized not as dataset observations but as concatenations of concrete historical events that produce a specific outcome ( Reference Mahoney Goertz and Mahoney 2012 ). That is, cases are increasingly treated as social processes, where a process is defined as “a particular type of sequence in which the temporally ordered events belong to a single coherent pattern of activity” ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 214). Although there exist multiple distinct conceptions of process tracing – from Bayesian approaches ( Reference Bennett, Bennett and Checkel Bennett 2015 ) to set-theoretic approaches ( Reference Mahoney, Kimball and Koivu Mahoney et al. 2009 ) to mechanistic approaches ( Reference Beach and Pedersen Beach and Pedersen 2013 ) to sequentialist approaches ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 ) – their overall esprit is the same: reconstructing the sequence of events and interlinking causal logics that produce an outcome – isolating the ‘causes of effects’ – rather than probing a variable’s mean impact across cases via an ‘effects of causes’ approach. Footnote 4

For this intellectual shift to occur, processualist social scientists had to show how a number of assumptions underlying Millian comparative methods – as well as frequentist approaches more generally – are usually inappropriate for case study research. For example, the correlational approach endorsed by Reference Przeworski and Teune Przeworski and Teune (1970) , Reference Lijphart Lijphart (1971) , and Reference Eckstein, Greenstein and Polsby Eckstein (1975) treats observational units as homogeneous and independent ( Reference Hall, Mahoney and Rueschemeyer Hall 2003 : 382; Reference Mahoney Goertz and Mahoney 2012 ). Unit homogeneity means that “different units are presumed to be fully identical to each other in all relevant respects except for the values of the main independent variable,” such that each observation contributes equally to the confidence we have in the accuracy and magnitude of our causal estimates ( Reference Brady and Collier Brady and Collier 2010 : 41–42). Given this assumption, more observations are better – hence, Reference Lijphart Lijphart (1971) ’s dictum to “increase the number of cases” and, in its more recent variant, to “increase the number of observations” ( Reference King, Keohane and Verba King, Keohane, and Verba 1994 : 208–230). By independence, we mean that “for each observation, the value of a particular variable is not influenced by its value in other observations”; thus, each observation contributes “new information about the phenomenon in question” ( Reference Brady and Collier Brady and Collier 2010 : 43).

By contrast, practitioners of process tracing have shown that treating cases as social processes implies that case study observations are often interdependent and derived from heterogeneous units ( Reference Mahoney Goertz and Mahoney 2012 ). Unit heterogeneity means that not all historical events, and the observable evidence they generate, are created equal. Hence, some observations may better enable the reconstruction of a causal process because they are more proximate to the central events under study. Correlatively, this is why historians accord greater ‘weight’ to primary than to secondary sources, and why primary sources concerning actors central to a key event are more important than those for peripheral figures ( Reference Trachtenberg Trachtenberg 2009 ; Reference Tansey Tansey 2007 ). In short, while process tracing may yield a bounty of observable evidence, we seek not to necessarily increase the number, but rather the quality, of observations. Finally, by interdependence we mean that because time is “fateful” ( Reference Sewell Sewell 2005 : 6), antecedent events in a sequence may influence subsequent events. This “fatefulness” has multiple sources. For instance, historical institutionalists have shown how social processes can exhibit path dependencies where the outcome of interest becomes a central driver of its own reproduction ( Reference Pierson Pierson 1996 ; Reference Pierson Pierson 2000 ; Reference Mahoney Mahoney 2000 ; Reference Hall, Mahoney and Rueschemeyer Hall 2003 ; Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 ). At the individual level, processual sociologists have noted that causation in the social world is rarely a matter of one billiard ball hitting another, as in Reference Hume Hume’s (1738 [2003]) frequentist concept of “constant conjunction.” Rather, it hinges upon actors endowed with memory, such that the micro-foundations of social causation rest on individuals aware of their own historicality ( Reference Sewell Sewell 2005 ; Reference Abbott Abbott 2001 ; Reference Abbott 2016 ).

At its core, eschewing the independence and unit homogeneity assumptions simply means situating case study evidence within its spatiotemporal context ( Reference Hall, Mahoney and Rueschemeyer Hall 2003 ; Reference Falleti and Lynch Falleti and Lynch 2009 ). This commitment is showcased by the language which process-sensitive case study researchers use when making causal inferences. First, rather than relating ‘independent variables’ to ‘dependent variables’, they often privilege the contextualizing language of relating ‘events’ to ‘outcomes’ ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 ). Second, they prefer to speak not of ‘dataset observations’ evocative of cross-sectional analysis, but of ‘causal process observations’ evocative of sequential analysis ( Reference Brady and Collier Brady and Collier 2010 ; Reference Mahoney Goertz and Mahoney 2012 ). Third, they may substitute the language of ‘causal inference via concatenation’ – a terminology implying that unobservable causal mechanisms are embedded within a sequence of observable events – for that of ‘causal inference via correlation’, evocative of the frequentist billiard-ball analogy ( Reference Waldner and Kincaid Waldner 2012 : 68). The result is that case study research is increasingly hailed as a “distinctive approach that offers a much richer set of observations, especially about causal processes, than statistical analyses normally allow” ( Reference Hall, Mahoney and Rueschemeyer Hall 2003 : 397).

7.3 Threats to Processual Inference and the Role of Theory

While scholars have shown how process-tracing methods have reconceived the utility of case studies for causal inference, there remains some ambiguity about the implications for case selection, particularly using Millian methods. While several works have touched upon this theme (e.g., Reference Hall, Mahoney and Rueschemeyer Hall 2003 ; Reference George and Bennett George and Bennett 2005 ; Reference Levy Levy 2008 ; Reference Tarrow Tarrow 2010 ), the contribution that most explicitly wrestles with this topic is Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney (2015) , who acknowledge that “the application of Millian methods for sequential arguments has not been systematically explored, although we believe it is commonly used in practice” ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 226). Falleti and Mahoney argue that process tracing can remedy the weaknesses of Millian approaches: “When used in isolation, the methods of agreement and difference are weak instruments for small-N causal inference … small-N researchers thus normally must combine Millian methods with process tracing or other within-case methods to make a positive case for causality” ( Reference Falleti, Mahoney, Mahoney and Thelen 2015 : 225–226). Their optimism about the synergy between Millian methods and process tracing leads them to conclude that “by fusing these two elements, the comparative sequential method merits the distinction of being the principal overarching methodology for [comparative-historical analysis] in general” ( Reference Falleti, Mahoney, Mahoney and Thelen 2015 : 236).

Falleti and Mahoney’s contribution is the definitive statement of how comparative case study research has long abandoned its Lijphartian origins and fully embraced treating cases as social processes. It is certainly true that process-tracing advocates have shown that some past critiques of Millian methods may not have been as damning as they first appeared. For example, Reference Lieberson Lieberson’s (1994) critique that Millian case selection requires a deterministic understanding of causation has been countered by set-theoretic process tracers who note that causal processes can indeed be conceptualized as concatenations of necessary and sufficient conditions ( Reference Mahoney Goertz and Mahoney 2012 ; Reference Mahoney and Vanderpoel Mahoney and Vanderpoel 2015 ). After all, “at the individual case level, the ex post (objective) probability of a specific outcome occurring is either 1 or 0” ( Reference Mahoney Mahoney 2008 : 415). Even for those who do not explicitly embrace set-theoretic approaches and prefer to perform a series of “process tracing tests” (such as straw-in-the-wind, hoop, smoking gun, and doubly-decisive tests), the objective remains to evaluate the deterministic causal relevance of a historical event on the next linkage in a sequence ( Reference Collier Collier 2011 ; Reference Mahoney Mahoney 2012 ). In this light, Millian methods appear to have been thrown a much-needed lifeline.

Yet processualist researchers have implicitly exposed new, and perhaps more damning, weaknesses in the traditional use of the comparative method. Here, Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney (2015) are less engaged in highlighting how their focus on comparing within-case sequences should push scholars to revisit strategies for case selection premised on assumptions that process-tracing advocates have undermined. In this light, I begin by outlining three hitherto underappreciated threats to inference associated with the traditional use of Millian case selection: potentially ignoring (1) ordered and (2) paced causal processes, and ignoring (3) the possibility of equifinality. I then demonstrate how risks (1) and (2) can be attenuated deductively by formulating processualist theories and tweaking Millian designs for case selection.

Risk 1: Ignoring Ordered Processes

Process-sensitive social scientists have long noted that “the temporal order of the events in a sequence [can be] causally consequential for the outcome of interest” ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 218; see also Reference Pierson Pierson 2004 : 54–78). For example, where individual acts of agency play a critical role – such as political elites’ response to a violent protest – “reordering can radically change [a] subject’s understanding of the meaning of particular events,” altering their response and the resulting outcomes ( Reference Abbott Abbott 1995 : 97).

An evocative illustration is provided by Reference Sewell Sewell’s (1996) analysis of how the storming of the Bastille in 1789 produced the modern concept of “revolution.” After overrunning the fortress, the crowd freed the few prisoners held within it; shot, stabbed, and beheaded the Bastille’s commander; and paraded his severed head through the streets of Paris ( Reference Sewell Sewell 1996 : 850). When the French National Assembly heard of the taking of the Bastille, it first interpreted the contentious event as “disastrous news” and an “excess of fury”; yet, when the king subsequently responded by retreating his troops to their provincial barracks, the Assembly recognized that the storming of the Bastille had strengthened its hand, and proceeded to reinterpret the event as a patriotic act of protest in support of political change ( Reference Sewell Sewell 1996 : 854–855). The king’s reaction to the Bastille thus bolstered the Assembly’s resolve to “invent” the modern concept of revolution as a “legitimate rising of the sovereign people that transformed the political system of a nation” ( Reference Sewell Sewell 1996 : 854–858). Proceeding counterfactually, had the ordering of events been reversed – had the king withdrawn his troops before the Bastille had been stormed – the National Assembly would have had little reason to interpret the popular uprising as a patriotic act legitimating reform rather than a violent act of barbarism.

Temporal ordering may also alter a social process’s political outcomes through macro-level mechanisms. For example, consider Reference Falleti Falleti’s (2005 , Reference Falleti 2010 ) analysis of the conditions under which state decentralization – the devolution of national powers to subnational administrative bodies – increases local political autonomy in Latin America. Through process tracing, Falleti demonstrates that when fiscal decentralization precedes electoral decentralization, local autonomy is increased, since this sequence endows local districts with the monetary resources necessary to subsequently administer an election effectively. However, when the reverse occurs, such that electoral decentralization precedes fiscal decentralization, local autonomy is compromised. For although the district is being offered the opportunity to hold local elections, it lacks the monetary resources to administer them effectively, endowing the national government with added leverage to impose conditions upon the devolution of fiscal resources.

For our purposes, what is crucial to note is not simply that temporal ordering matters, but that in ordered processes it is not the presence or absence of events that is most consequential for the outcome of interest. For instance, in Falleti’s analysis both fiscal and electoral decentralization occur. This means that a traditional Millian framework risks dismissing some explanatory events as causally irrelevant on the grounds that their presence is insufficient for explicating the outcome of interest (see Figure 7.2 ).

Figure 7.2 How ordered processes risk being ignored by a Millian setup

The way to deductively attenuate the foregoing risk is to develop an ordered theory and then modify the traditional Millian setup to assess the effect of ordering on an outcome of interest. That is, deductive theorizing aimed at probing the causal effect of ordering can guide us in constructing an appropriate Millan case selection design, such as that in Figure 7.3 . In this example, we redefine the fourth independent variable to measure not the presence or absence of a fourth event, but rather to measure the ordering of two previously defined events (in this case, events 1 and 2). This case selection setup would be appropriate if deductive theorizing predicts that the outcome of interest is produced when event 1 is followed by event 2 (such that, unless this specific ordering occurs, the presence of events 1 and 2 is insufficient to generate the outcome). In other words, if Millian methods are to be deductively used to select cases for comparison, the way to guard against prematurely dismissing the causal role of temporal ordering is to explicitly theorize said ordering a priori . If this proves difficult, or if the researcher lacks sufficient knowledge to develop such a theory, it is advisable to switch to the more inductive method for case selection outlined in the next section .

Figure 7.3 Deductively incorporating ordered processes within a Millian setup

Risk 2: Ignoring Paced Processes

Processualist researchers have also emphasized that, beyond temporal order, “the speed or duration of events … is causally consequential” ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 219). For example, social scientists have long distinguished an “eventful temporality” ( Reference Sewell Sewell 1996 ) from those “big, slow moving” incremental sequences devoid of rapid social change ( Reference Pierson, Mahoney and Rueschemeyer Pierson 2003 ). For historical institutionalists, this distinction is illustrated by “critical junctures” – defined as “relatively short periods of time during which there is a substantially heightened probability that agents’ choices will affect the outcome of interest” ( Reference Capoccia and Kelemen Capoccia and Kelemen 2007 : 348; Reference Capoccia, Mahoney and Thelen Capoccia 2015 : 150–151) – on the one hand, and those “causal forces that develop over an extended period of time,” such as “cumulative” social processes, sequences involving “threshold effects,” and “extended causal chains” on the other hand ( Reference Pierson Pierson 2004 : 82–90; Reference Mahoney, Thelen, Mahoney and Thelen Mahoney and Thelen 2010 ).

An excellent illustration is provided by Reference Beissinger Beissinger (2002) ’s analysis of the contentious events that led to the collapse of the Soviet State. Descriptively, the sequence of events has its origins in the increasing transparency of Soviet institutions and freedom of expression accompanying Gorbachev’s Glasnost ( Reference Beissinger Beissinger 2002 : 47). As internal fissures within the Politburo began to emerge in 1987, Glasnost facilitated media coverage of the split within the Soviet leadership ( Reference Beissinger 2002 : 64). In response, “interactive attempts to contest the state grew regularized and began to influence one another” ( Reference Beissinger 2002 : 74). These challenging acts mobilized around previously dormant national identities, and for the first time – often out of state incompetence – these early protests were not shut down ( Reference Beissinger 2002 : 67). Protests reached a boiling point in early 1989 as the first semicompetitive electoral campaign spurred challengers to mobilize the electorate and cultivate grievances in response to regime efforts to “control nominations and electoral outcomes” ( Reference Beissinger 2002 : 86). By 1990 the Soviet State was crumbling, and “in many parts of the USSR demonstration activity … had become a normal means for dealing with political conflict” ( Reference Beissinger 2002 : 90).

Crucially, Beissinger stresses that to understand the causal dynamics of the Soviet State’s collapse, highlighting the chronology of events is insufficient. The 1987–1990 period comprised a moment of “thickened history” wherein “what takes place … has the potential to move history onto tracks otherwise unimaginable … all within an extremely compressed period of time” ( Reference Beissinger 2002 : 27). Information overload, the density of interaction between diverse social actors, and the diffusion of contention engendered “enormous confusion and division within Soviet institutions,” allowing the hypertrophy of challenging acts to play “an increasingly significant role in their own causal structure” ( Reference Beissinger 2002 : 97, 27). In this light, the temporal compression of a sequence of events can bolster the causal role of human agency and erode the constraints of social structure. Proceeding counterfactually, had the exact same sequence of contentious events unfolded more slowly, it is doubtful that the Soviet State would have suddenly collapsed.

Many examples of how the prolongation of a sequence of events can render them invisible, and thus produce different outcomes, could be referenced. Consider, for example, how global climate change – which is highlighted by Reference Pierson Pierson (2004 : 81) as a prototypical process with prolonged time horizons – conditions the psychological response of social actors. As a report from the American Psychological Association underscores, “climate change that is construed as rapid is more likely to be dreaded,” for “people often apply sharp discounts to costs or benefits that will occur in the future … relative to experiencing them immediately” ( Reference Swim Swim et al. 2009 : 24–25; Reference Loewenstein and Elster Loewenstein and Elster 1992 ). This logic is captured by the metaphor of the “boiling frog”: “place a frog in a pot of cool water, and gradually raise the temperature to boiling, and the frog will remain in the water until it is cooked” ( Reference Boyatzis Boyatzis 2006 : 614).

What is important to note is that, once more, paced processes are not premised on the absence or presence of their constitutive events being causally determinative; rather, they are premised on the duration of events (or their temporal separation) bearing explanatory significance. Hence the traditional approach to case selection risks neglecting the causal impact of temporal duration on the outcome of interest (see Figure 7.4 ).

Figure 7.4 Paced processes risk being ignored by a Millian setup

Here, too, the way to deductively assess the causal role of pacing on an outcome of interest is to explicitly develop a paced theory before selecting cases for empirical analysis. On the one hand, we might theorize that it is the duration of a given event that is causally consequential; on the other hand, we might theorize that it is the temporal separation of said event from other events that is significant. Figure 7.5 suggests how a researcher can assess both theories through a revised Millian design. In the first example, we define a fourth independent variable measuring not the presence of a fourth event, but rather the temporal duration of a previously defined event (in this case, event 1). This would be an appropriate case selection design to assess a theory predicting that the outcome of interest occurs when event 1 unfolds over a prolonged period of time (such that if event 1 unfolds more rapidly, its mere occurrence is insufficient for the outcome). In the second example, we define a fourth independent variable measuring the temporal separation between two previously defined events (in this case, events 1 and 2). This would be an appropriate case selection design for a theory predicting that the outcome of interest only occurs when event 1 is temporally distant to event 2 (such that events 1 and 2 are insufficient for the outcome if they are proximate). Again, if the researcher lacks a priori knowledge to theorize how a paced process may be generating the outcome, it is advisable to adopt the inductive method of case selection described in Section 7.4 .

Figure 7.5 Deductively incorporating paced processes within a Millian setup

Risk 3: Ignoring Equifinal Causal Processes

Finally, researchers have noted that causal processes may be mired by equifinality: the fact that “multiple combinations of values … produce the same outcome” ( Reference Mahoney Mahoney 2008 : 424; see also Reference George and Bennett George and Bennett 2005 ; Reference Mahoney Goertz and Mahoney 2012 ). More formally, set-theoretic process tracers account for equifinality by emphasizing that, in most circumstances, “necessary” conditions or events are actually INUS conditions – individually necessary components of an unnecessary but sufficient combination of factors ( Reference Mahoney and Vanderpoel Mahoney and Vanderpoel 2015 : 15–18).

One of the reasons why processualist social scientists increasingly take equifinality seriously is the recognition that causal mechanisms may be context-dependent. Sewell’s work stresses that “the consequences of a given act … are not intrinsic to the act but rather will depend on the nature of the social world within which it takes place” ( Reference Sewell Sewell 2005 : 9–10). Similarly, Reference Falleti and Lynch Falleti and Lynch (2009 : 2; 11) argue that “causal effects depend on the interaction of specific mechanisms with aspects of the context within which these mechanisms operate,” hence the necessity of imposing “scope conditions” on theory building. One implication is that the exact same sequence of events in two different settings may produce vastly different causal outcomes. The flip side of this conclusion is that we should not expect a given outcome to always be produced by the same sequence of events.

For example, consider Sewell’s critique of Reference Skocpol Skocpol (1979) ’s States and Social Revolutions for embracing an “experimental temporality.” Skocpol deploys Millian methods of case selection to theorize that the great social revolutions – the French, Russian, and Chinese revolutions – were caused by a conjunction of three necessary conditions: “(1) military backwardness, (2) politically powerful landlord classes, and (3) autonomous peasant communities” ( Reference Sewell Sewell 2005 : 93). Yet to permit comparison, Skocpol assumes that the outcomes of one revolution, and the processes of historical change more generally, have no effect on a subsequent revolution ( Reference Sewell Sewell 2005 : 94–95). This approach amounts to “cutting up the congealed block of historical time into artificially interchangeable units,” ignoring the fatefulness of historical sequences ( Reference Sewell Sewell 2005 ). For example, the Industrial Revolution “intervened” between the French and Russian Revolutions, and consequently one could argue that “the revolt of the Petersburg and Moscow proletariat was a necessary condition for social revolution in Russia in 1917, even if it was not a condition for the French Revolution in 1789” ( Reference Sewell Sewell 2005 : 94–95). What Sewell is emphasizing, in short, is that peasant rebellion is an INUS condition (as is a proletariat uprising), rather than a necessary condition.

Another prominent example of equifinality is outlined by Reference Collier Collier’s (1999 : 5–11) review of the diverse pathways through which democratization occurs. In the elite-driven pathway, emphasized by Reference O’Donnell and Schmitter O’Donnell and Schmitter (1986 ), an internal split amongst authoritarian incumbents emerges; this is followed by liberalizing efforts by some incumbents, which enables the resurrection of civil society and popular mobilization; finally, authoritarian incumbents negotiate a pacted transition with opposition leaders. By contrast, in the working-class-driven pathway, emphasized by Reference Rueschemeyer, Stephens and Stephens Rueschemeyer, Stephens, and Stephens (1992) , a shift in the material balance of power in favor of the democracy-demanding working class and against the democracy-resisting landed aristocracy causes the former to overpower the latter, and via a democratic revolution from below a regime transition occurs. Crucially, Reference Collier Collier (1999 : 12) emphasizes that these two pathways need not be contradictory (or exhaustive): the elite-driven pathway appears more common in the Latin American context during the second wave of democratization, whereas the working-class-driven pathway appears more common in Europe during the first wave of democratization.

What is crucial is that Millian case selection is premised on there being a single cause underlying the outcome of interest. As a result, Millian methods risk dismissing a set of events as causally irrelevant ex ante in one case simply because that same set of events fails to produce the outcome in another case (see Figure 7.6 ). Unlike ordered and paced processes, there is no clear way to leverage deductive theorizing to reconfigure Millian methods for case selection and accommodate equifinality. However, I argue that the presence of equifinal pathways can be fruitfully probed if we embrace a more inductive approach to comparative case selection, as the next section outlines.

Figure 7.6 Equifinal causal processes risk being ignored by a Millian setup

7.4 A New Approach: The Method of Inductive Case Selection

If a researcher wishes to guard against ignoring consequential temporal dynamics but lacks the a priori knowledge necessary to develop a processual theory and tailor their case selection strategy, is there an alternative path forward? Yes, indeed: I suggest that researchers could wield most-similar or most-different cases designs to (1) probe causal generalizability, (2) reveal scope conditions, and (3) explore the presence of equifinality. Footnote 5 To walk through this more inductive case selection approach, I engage some case studies from development practice to illustrate how researchers and practitioners alike could implement and benefit from the method.

7.4.1 Tempering the Deductive Use of Millian Methods

To begin, one means to ensure against a Millian case selection design overlooking an ordered, paced, or equifinal causal process (in the absence of deductive theorizing) is to be wary of leveraging the methods of agreement and difference to eliminate potential explanatory factors ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 225–226). That is, the decision to discard an explanatory variable or historical event as causally unnecessary (via the method of agreement) or insufficient (via the method of difference) may be remanded to the process-tracing stage, rather than being made ex ante at the case selection stage.

Notice how this recommendation is particularly intuitive in light of the advances in process-tracing methods. Before this burgeoning literature existed, Millian methods were called upon to accomplish two things at once: (1) provide a justification for selecting two or more cases for social inquiry, and (2) yield causal leverage via comparison and the elimination of potential explanatory factors as unnecessary or insufficient. But process-tracing methodologists have showcased how the analysis of temporal variation disciplined via counterfactual analysis, congruence testing, and process-tracing tests renders within-case causal inference possible even in the absence of an empirical comparative case ( Reference George and Bennett George and Bennett 2005 ; Reference Gerring Gerring 2007 ; Reference Collier Collier 2011 ; Reference Mahoney Mahoney 2012 ; Reference Beach and Pedersen Beach and Pedersen 2013 ; Reference Bennett and Checkel Bennett and Checkel 2015 ; Reference Levy Levy 2015 ). That is, the ability to make causal inferences need not be primarily determined at the case selection stage.

The foregoing implies that if a researcher does not take temporal dynamics into account when developing their theory, the use of Millian methods should do no more than to provisionally discount the explanatory purchase of a given explanatory factor. The researcher should then bear in mind that as the causal process is reconstructed from a given outcome, the provisionally discounted factor may nonetheless be shown to be of causal relevance – particularly if the underlying process is ordered or paced, or if equifinal pathways are possible.

Despite these limitations, Millian methods might fruitfully serve additional functions from the standpoint of case selection, particularly if researchers shift (1) when and (2) why they make use of them. First, Millian methods may be as – if not more – useful after process tracing of a particular case is completed rather than to set the stage for within-case analysis. Such a chronological reversal – process tracing followed by Millian case selection, instead of Millian case selection followed by process tracing – inherently embraces a more inductive, theory-building approach to case study research ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 229–231) which, I suspect, is far more commonly used in practice than is acknowledged. I refer to this approach as the method of inductive case selection , wherein “theory-building process tracing” ( Reference Beach and Pedersen Beach and Pedersen 2013 : 16–18) of a single case is subsequently followed by the use of a most-similar or most-different cases design.

7.4.2 Getting Started: Selecting the Initial Case

The method of inductive case selection begins by assuming that the researcher has justifiable reasons for picking a particular case for process tracing and is subsequently looking to contextualize the findings or build a theory outwards. Hence, the first step involves picking an initial case. Qualitative methodologists have already supplied a number of plausible logics for selecting a single case, and I describe three nonexhaustive possibilities here: (1) theoretical or historical importance; (2) policy relevance and salience; and (3) empirically puzzling nature.

First, an initial case may be selected due to its theoretical or historical importance. Reference Eckstein, Greenstein and Polsby Eckstein (1975) , for example, defines an idiographic case study as a case where the specific empirical events/outcome serve as a central referent for a scholarly literature. As an illustration, Reference Gerring and Cojocaru Gerring and Cojocaru (2015 : 11) point to Reference North and Weingast North and Weingast (1989) ’s influential study of how the Glorious Revolution in seventeenth-century Britain favorably shifted the constitutional balance of power for the government to make credible commitments to protecting property rights (paving the way for the financial revolution of the early eighteenth century). Given that so much of the scholarly debate amongst economic historians centers on the institutional foundations of economic growth, North and Weingast’s case study was “chosen (it would appear) because of its central importance in the [historical political economy] literature on the topic, and because it is … a prominent and much-studied case” ( Reference Gerring and Cojocaru Gerring and Cojocaru 2015 : 11). In other words, Reference North and Weingast North and Weingast (1989) ’s study is idiographic in that it “aim[s] to explain and/or interpret a single historical episode,” but it remains “theory-guided” in that it “focuses attention on some theoretically specified aspects of reality and neglects others” ( Reference Levy Levy 2008 : 4).

While the causes of the Glorious Revolution are a much-debated topic amongst economic historians, they have less relevance to researchers and practitioners focused on assessing the effects of contemporary public policy interventions. Hence, a second logic for picking a first case for process tracing is its policy relevance and salience. Reference George and Bennett George and Bennett (2005 : 263–286) define a policy-relevant case study as one where the outcome is of interest to policy-makers and its causes are at least partially amenable to policy manipulation. For example, one recent World Bank case study ( Reference El-Saharty and Nagaraj El-Saharty and Nagaraj 2015 ) analyzes how HIV/AIDS prevalence amongst vulnerable subpopulations – particularly female sex workers – can be reduced via targeted service delivery. To study this outcome, two states in India – Andhra Pradesh and Karnataka – were selected for process tracing. There are three reasons why this constitutes an appropriate policy-relevant case selection choice. First, the outcome of interest – a decline in HIV/AIDS prevalence amongst female sex workers – was present in both Indian states. Second, because India accounts for almost 17.5 percent of the world population and has a large population of female sex workers, this outcome was salient to the government ( Reference El-Saharty and Nagaraj El-Saharty and Nagaraj 2015 : 3). Third, the Indian government had created a four-phase National AIDS Control Program (NACP) spanning from 1986 through 2017, meaning that at least one set of possible explanatory factors for the decline in HIV/AIDS prevalence comprised policy interventions that could be manipulated. Footnote 6

A third logic for picking an initial case for process tracing is its puzzling empirical nature. One obvious instantiation is when an exogenous shock or otherwise significant event/policy intervention yields a different outcome from the one scholars and practitioners expected. Footnote 7 For example, in 2004 the federal government of Nigeria partnered with the World Bank to improve the share of Nigeria’s urban population with access to piped drinking water. This partnership – the National Urban Water Sector Reform Project (NUWSRP1) – aimed to “increase access to piped water supply in selected urban areas by improving the reliability and financial viability of selected urban water utilities” and by shifting resources away from “infrastructure rehabilitation” that had failed in the past ( Reference Hima and Santibanez Hima and Santibanez 2015 : 2). Despite $200 million worth of investments, ultimately the NUWSRP1 “did not perform as strongly on the institutional reforms needed to ensure sustainability” ( Reference Hima and Santibanez Hima and Santibanez 2015 ). Given this puzzling outcome, the World Bank conducted an intensive case study to ask why the program did “not fully meet its essential objective of achieving a sustainable water delivery service” ( Reference Hima and Santibanez Hima and Santibanez 2015 ). Footnote 8

The common thread of these three logics for selecting an initial case is that the case itself is theoretically or substantively important and that its empirical dynamics – underlying either the outcome itself or its relationship to some explanatory events – are not well understood. That being said, the method of inductive case selection merely presumes that there is some theoretical, policy-related, empirical, or normative justification to pick the initial case.

7.4.3 Probing Generalizability Via a Most-Similar Cases Design

It is after picking an initial case that the method of inductive case selection contributes novel guidelines for case study researchers by reconfiguring how Millian methods are used. Namely, how should one (or more) additional cases be selected for comparison, and why? This question presumes that the researcher wishes to move beyond an idiographic, single-case study for the purposes of generating inferences that can travel. Yet in this effort, we should take seriously process-tracing scholars’ argument that causal mechanisms are often context-dependent. As a result, the selection of one or more comparative cases is not meant to uncover universally generalizable abstractions; rather, it is meant to contextualize the initial case within a set or family of cases that are spatiotemporally bounded.

That being said, the first logical step is to understand whether the causal inferences yielded by the process-traced case can indeed travel to other contexts ( Reference Goertz Goertz 2017 : 239). This constitutes the first reconfiguration of Millian methods: the use of comparative case studies to assess generalizability. Specifically, after within-case process tracing reveals a factor or sequence of factors as causally important to an outcome of interest, the logic is to select a case that is as contextually analogous as possible such that there is a higher probability that the causal process will operate similarly in the second case. This approach exploits the context-dependence of causal mechanisms to the researcher’s advantage: Similarity of context increases the probability that a causal mechanism will operate similarly across both cases. By “context,” it is useful to follow Reference Falleti and Lynch Falleti and Lynch (2009 : 14) and to be

concerned with a variety of contextual layers: those that are quite proximate to the input (e.g., in a study of the emergence of radical right-wing parties, one such layer might be the electoral system); exogenous shocks quite distant from the input that might nevertheless effect the functioning of the mechanism and, hence, the outcome (e.g., a rise in the price of oil that slows the economy and makes voters more sensitive to higher taxes); and the middle-range context that is neither completely exogenous nor tightly coupled to the input and so may include other relevant institutions and structures (the tax system, social solidarity) as well as more atmospheric conditions, such as rates of economic growth, flows of immigrants, trends in partisan identification, and the like.

For this approach to yield valuable insights, the researcher focuses on ‘controlling’ for as many of these contextual explanatory factors (crudely put, for as many independent variables) as possible. In other words, the researcher selects a most-similar case: if the causal chain similarly operates in the second case, this would support the conclusion that the causal process is likely at work across the constellation of cases bearing ‘family resemblances’ to the process-traced case ( Reference Soifer Soifer 2020 ). Figure 7.7 displays the logic of this design:

Figure 7.7 Probing generalizability by selecting a most-similar case

As in Figure 7.7 , suppose that process tracing of Case 1 reveals that some sequence of events (in this example, event 4 followed by event 5) caused the outcome of interest. The researcher would then select a most-similar case (a case with similar values/occurrences of other independent variables/events (here, IV1–IV3) that might also influence the outcome). The researcher would then scout whether the sequence in Case 1 (event 4 followed by event 5) also occurs in the comparative case. If it does, the expectation for a minimally generalizable theory is that it would produce a similar outcome in Case 2 as in Case 1. Correlatively, if the sequence does not occur in Case 2, the expectation is that it would not experience the same outcome as Case 1. These findings would provide evidence that the explanatory sequence (event 4 followed by event 5) has causal power that is generalizable across a set of cases bearing family resemblances.

For example, suppose a researcher studying democratization in Country A finds evidence congruent with the elite-centric theory of democratization of Reference O’Donnell and Schmitter O’Donnell and Schmitter (1986 ) described previously. To assess causal generalizability, the researcher would subsequently select a case – Country B – that is similar in the background conditions that the literature has shown to be conducive to democratization, such as level of GDP per capita ( Reference Przeworski and Limongi Przeworski and Limongi 1997 ; Reference Boix and Stokes Boix and Stokes 2003 ) or belonging to the same “wave” of democratization via spatial and temporal proximity ( Reference Collier, Rustow and Erickson Collier 1991 ; Reference Huntington Huntington 1993 ). Notice that these background conditions in Case B have to be at least partially exogenous to the causal process whose generalizability is being probed – that is, they cannot constitute the events that directly comprise the causal chain revealed in Case A. One way to think about them is as factors that in Case A appear to have been necessary, but less proximate and important, conditions for the outcome. Here, importance is determined by the “extent that they are [logically/counterfactually] present only when the outcome is present” ( Reference Mahoney, Kimball and Koivu Mahoney et al. 2009 : 119), whereas proximity is determined by the degree to which the condition is “tightly coupled” with the chain of events directly producing the outcome ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 233).

An example related to the impact of service delivery in developmental contexts can be drawn from the World Bank’s case study of HIV/AIDS interventions in India. Recall that this case study actually spans across two states: Andhra Pradesh and Karnataka. In a traditional comparative case study setup, the selection of both cases would seem to yield limited insights. After all, they are contextually similar: “Andhra Pradesh and Karnataka … represent the epicenter of the HIV/AIDS epidemic in India. In addition, they were early adopters of the targeted interventions”; and they also experience a similar outcome: “HIV/AIDS prevalence among female sex workers declined from 20 percent to 7 percent in Andhra Pradesh and from 15 percent to 5 percent in Karnataka between 2003 and 2011” ( Reference El-Saharty and Nagaraj El-Saharty and Nagaraj 2015 : 7; 3). In truth, this comparative case study design makes substantial sense: had the researchers focused on the impact of the Indian government’s NACP program only in Andhra Pradesh or only in Karnataka, one might have argued that there was something unique about either state that rendered it impossible to generalize the causal inferences. By instead demonstrating that favorable public health outcomes can be traced to the NACP program in both states, the researchers can support the argument that the intervention would likely prove successful in other contexts to the extent that they are similar to Andhra Pradesh and Karnataka.

One risk of the foregoing approach is highlighted by Reference Sewell Sewell (2005 : 95–96): contextual similarity may suggest cross-case interactions that hamper the ability to treat the second, most-similar case as if it were independent of the process-traced case. For example, an extensive body of research has underscored how protests often diffuse across proximate spatiotemporal contexts through mimicry and the modularity of repertoires of contention ( Reference Tilly Tilly 1995 ; Reference Tarrow Tarrow 1998 ). And, returning to the World Bank case study of HIV/AIDS interventions in Andhra Pradesh and Karnataka, one concern is that because these states share a common border, cross-state learning or other interactions might limit the value-added of a comparative design over a single case study, since the second case may not constitute truly new data. The researcher should be highly sensitive to this possibility when selecting and subsequently process tracing the most-similar case: the greater the likelihood of cross-case interactions, the lesser the likelihood that it is a case-specific causal process – as opposed to cross-case diffusion mechanism – that is doing most of the explanatory work.

Conversely, if the causal chain is found to operate differently in the second, most-similar case, then the researcher can make an argument for rejecting the generalizability of the causal explanation with some confidence. The conclusion would be that the causal process is sui generis and requires the “localization” of the theoretical explanation for the outcome of interest ( Reference Tarrow Tarrow 2010 : 251–252). In short, this would suggest that the process-traced case is an exceptional or deviant case, given a lack of causal generalizability even to cases bearing strong family resemblances. Here, we are using the ‘strong’ notion of ‘deviant’: the inability of a causal process to generalize to similar contexts substantially decreases the likelihood that “other cases” could be explained with reference to (or even in opposition to) the process-traced case.

There is, of course, the risk that by getting mired in the weeds of the first case, the researcher is unable to recognize how the overall chronology of events and causal logics in the most-similar case strongly resembles the process-traced case. That is, a null finding of generalizability in a most-similar context calls on the researcher to probe whether they have descended too far down the “ladder of generality,” requiring more abstract conceptual categories to compare effectively ( Reference Sartori Sartori 1970 ; Reference Collier and Levitsky Collier and Levitsky 1997 ).

7.4.4 Probing Scope Conditions and Equifinality Via a Most-Different Cases Design

A researcher that has process-traced a given case and revealed a factor or sequence of factors as causally relevant may also benefit from leveraging a most-different cases approach. This case selection technique yields complementary insights to the most-similar cases design described in the previous section , but its focus is altogether different: instead of uncovering the degree to which an identified causal process travels, the objective is to try to understand where and why it fails to travel and whether alternative pathways to the same outcome may be possible.

More precisely, by selecting a case that differs substantially from the process-traced case in background characteristics, the researcher maximizes contextual heterogeneity and the likelihood that the causal process will not generalize to the second case ( Reference Soifer Soifer 2020 ). Put differently, the scholar would be selecting a least-likely case for generalizability, because the context-dependence of causal mechanisms renders it unlikely that the same sequence of events will generate the same outcome in the second case. This would offer a first cut at establishing “scope conditions” upon the generalizability of the theory ( Reference Tarrow Tarrow 2010 : 251) by isolating which contextual factors prevented the process from producing the outcome in the most-different case.

Figure 7.8 provides a visual illustration of what this design could look like. Suppose, once more, that process tracing in Case 1 has revealed that some event 4 followed by event 5 generated the outcome of interest. To maximize the probability that we will be able to place scope conditions on this finding, we would select a comparative case that is most different to the process-traced case (a case with different values/occurrences of other independent variables/events [denoted as IV1–IV3 in Figure 7.8 ] that might also influence the outcome) but which also experienced the sequence of event 4 followed by event 5. Given the contextual differences between these two cases, the likelihood that the same sequence will produce the same outcome in both is low, which then opens up opportunities for the researcher to probe the logic of scope conditions. In this endeavor, temporality can serve as a useful guide: a means for restricting the set of potential contextual factors that prevented the causal process from reproducing the outcome in Case 2 is to identify at what chronological point the linkages between events 4 and 5 on the one hand and the outcome of interest on the other hand branched off from the way they unfolded in Case 1. The researcher can then scout which contextual factors exuded the greatest influence at that temporal location and identify them as central to the scope conditions to be placed upon the findings.

Figure 7.8 Probing scope conditions by selecting a most-different case

To provide an example for how this logic of inquiry can work, consider a recent case study focused on understanding the effectiveness of Mexico’s conditional cash transfer program – Opportunitades , the first program of its kind – in providing monetary support to the female heads of Indigenous households ( Reference Alva Estrabridis and Ortega Nieto Alva Estrabridis and Ortega Nieto 2015 ). The program suffered from the fact that Indigenous beneficiaries dropped out at higher rates than their non-Indigenous counterparts. In 2009 the World Bank spearheaded an Indigenous Peoples Plan (IPP) to bolster service delivery of cash transfers to Indigenous populations, which crucially included “catering to indigenous peoples in their native languages and disseminating information in their languages” ( Reference Alva Estrabridis and Ortega Nieto Alva Estrabridis and Ortega Nieto 2015 : 2). A subsequent impact evaluation found that “[w]hen program messages were offered in beneficiaries’ mother tongues, they were more convincing, and beneficiaries tended to participate and express themselves more actively” ( Reference Alva Estrabridis and Ortega Nieto Alva Estrabridis and Ortega Nieto 2015 ; Reference Mir, Gámez, Loyola, Martí and Veraza Mir et al. 2011 ).

Researchers might well be interested in the portability of the foregoing finding, in which case the previously described most-similar cases design is appropriate – for example, a comparison with the Familias en Accion program in Colombia may be undertaken ( Reference Attanasio, Battistin, Fitzsimons, Mesnard and Vera-Hernandez. Attanasio et al. 2005 ). But they might also be interested in the limits of the policy intervention – in understanding where and why it is unlikely to yield similar outcomes. To assess the scope conditions upon the “bilingualism” effect of cash transfer programs, a most-different cases design is appropriate. Thankfully, conditional cash transfer programs are increasingly common even in historical, cultural, and linguistic contexts markedly different from Mexico, most prominently in sub-Saharan Africa ( Reference Lagarde, Haines and Palmer Lagarde et al. 2007 ; Reference Garcia and Moore Garcia and Moore 2012 ). Selecting a comparative case from sub-Saharan Africa should prove effective for probing scope conditions: the more divergent the contextual factors, the less likely it is that the policy intervention will produce the same outcome in both contexts.

On the flip side, in the unlikely event that part or all of the causal process is nonetheless reproduced in the most-different case, the researcher would obtain a strong signal that they have identified one of those rare causal explanations of general scope. In coming to this conclusion, however, the researcher should be wary of “conceptual stretching” ( Reference Sartori Sartori 1970 : 1034), such that there is confidence that the similarity in the causal chain across the most-different cases lies at the empirical level and is not an artificial by-product of imprecise conceptual categories ( Reference Bennett and Checkel Bennett and Checkel 2015 : 10–11). Here process tracing, by pushing researchers to not only specify a sequence of “tightly-coupled” events ( Reference Falleti, Mahoney, Mahoney and Thelen Falleti and Mahoney 2015 : 233), but also to collect observable implications about the causal mechanisms concatenating these events, can guard against conceptual stretching. By opening the “black box” of causation through detailed within-case analysis, process tracing limits the researcher’s ability to posit “pseudo-equivalences” across contexts ( Reference Sartori Sartori 1970 : 1035).

Selecting a most-different case vis-à-vis the process-traced case is also an excellent strategy for probing equifinality – for maximizing the likelihood that the scholar will be able to probe multiple causal pathways to the same outcome. To do so, it is not sufficient to merely ensure divergence in background conditions; it is equally necessary to follow Mill’s method of agreement by ensuring that the outcome in the process-traced case is also present in the second, most-different case. By ensuring minimal variation in outcome, the scholar guarantees that process tracing the second case will lead to the desired destination; by ensuring maximal variation in background conditions, the scholar substantially increases the likelihood that process tracing will reveal a slightly or significantly different causal pathway to said destination. Should an alternative route to the outcome be found, then its generalizability could be assessed using the most-similar cases approach described previously.

Figure 7.9 visualizes what this case selection design might look like. Here, as in previous examples, suppose process tracing in Case 1 provides evidence that event 4 followed by event 5 produced the outcome of interest. The researcher then selects a case with the same outcome, but with different values/occurrences of some independent variables/events (in this case, IV1–IV3) that may influence the outcome. Working backwards from the outcome to reconstruct the causal chain that produced it, the researcher then probes whether (i) the sequence (event 4 followed by event 5) also occurred in Case 2, and (ii) whether the outcome of interest can be retraced to said sequence. Given the contextual dissimilarities between these most-different cases, such a finding is rather unlikely, which would subsequently enable to the researcher to probe whether some other factor (perhaps IV2/event 2 in the example of Figure 7.9 ) produced the outcome in the comparative case instead, which would comprise clear evidence of equifinality.

Figure 7.9 Probing equifinality by selecting a most-different case with the same outcome

To return to the concrete example of Mexico’s conditional cash transfer program’s successful outreach to marginalized populations via bilingual service provision, an alternative route to the same outcome might be unearthed if a cash transfer program without bilingual outreach implemented in a country characterized by different linguistic, gender, and financial decision-making norms proves similarly successful in targeting marginalized populations. Several factors – including recruitment procedures, the size of the cash transfers, the requirements for participation, and the supply of other benefits ( Reference Lagarde, Haines and Palmer Lagarde et al. 2007 : 1902) – could interact with the different setting to produce similar intervention outcomes, regardless of whether multilingual services are provided. Such a finding would suggest that these policy interventions can be designed in multiple ways and still prove effective.

To conclude, the method of inductive case selection complements within-case analysis by supplying a coherent logic for probing generalizability, scope conditions, and equifinality. To summarize, Figure 7.10 provides a roadmap of this approach to comparative case selection.

Figure 7.10 Case selection roadmap to assess generalizability, scope conditions, equifinality

In short, if the researcher has the requisite time and resources, a multistage use of Millian methods to conduct four comparative case studies could prove very fertile. The researcher would begin by selecting a second, most-similar case to assess causal generalizability to a family of cases similar to the process-traced case; subsequently, a third, most-different case would be selected to surface possible scope conditions blocking the portability of the theory to divergent contexts; and a fourth, most-different case experiencing the same outcome would be picked to probe equifinal pathways. This sequential, four-case comparison would substantially improve the researcher’s ability to map the portability and contours of both their empirical analysis and their theoretical claims. Footnote 9

7.5 Conclusion

The method of inductive case selection converts process tracing meant to simply “craft a minimally sufficient explanation of a particular outcome” into a methodology used to build and refine a causal theory – a form of “theory-building process-tracing” ( Reference Beach and Pedersen Beach and Pedersen 2013 : 16–18). Millian methods are called upon to probe the portability of a particular causal process or causal mechanism and to specify the logics of its relative contextual-dependence. In so doing, they enable theory-building without presuming that the case study researcher holds the a priori knowledge necessary to account for complex temporal dynamics at the deductive theorizing stage. Both of these approaches – deductive, processualist theorizing on the one hand, and the method of inductive case selection on the other hand – provide some insurance against Millian methods leading the researcher into ignoring the ordered, paced, or equifinal structure that may underlie the pathway(s) to the outcome of interest. But, I would argue, the more inductive approach is uniquely suited for research that is not only process-sensitive, but also open to novel insights supplied by the empirical world that may not be captured by existing theories.

Furthermore, case study research often does (and should!) proceed with the scholar outlining why an outcome is of interest, and then seeking ways to not only make inferences about what produced said outcome (via process tracing) but situating it within a broader empirical and theoretical landscape (via the method of inductive case selection). This approach pushes scholars to answer that pesky yet fundamental question – why should we care or be interested in this case/outcome? – before disciplining their drive for generalizable causal inferences. After all, the deductive use of Millian methods tells us nothing about why we should care about the cases selected, yet arguably this is an essential component of any case selection justification. By deploying a most-similar or most-different cases design after an initial case has been justifiably selected due to its theoretical or historical importance, policy relevance, or puzzling empirical nature, the researcher is nudged toward undertaking case study research yielding causal theories that are not only comparatively engaged, but also substantively interesting.

The method of inductive case selection is most useful when the foregoing approach constitutes the esprit of the case study researcher. Undoubtedly, deductively oriented case study research (see Reference Lieberman Lieberman 2005 ; Reference Lieberman, Mahoney and Thelen 2015 ) and traditional uses of Millian methods will continue to contribute to social scientific understanding. Nevertheless, the perils of ignoring important sequential causal dynamics – particularly in the absence of good, processualist theories – should caution researchers to proceed with the greatest of care. In particular, researchers should be willing to revise both theory building and research design to its more inductive variant should process tracing reveal temporal sequences that eschew the analytic possibilities of the traditional comparative method.

I would like to thank Jennifer Widner and Michael Woolcock for the invitation to write this chapter, and Daniel Ortega Nieto for pointing me to case studies conducted by the World Bank’s Global Delivery Initiative that I use as illustrative examples, as well as Jack Levy, Hillel Soifer, Andrew Moravcsik, Cassandra Emmons, Rory Truex, Dan Tavana, Manuel Vogt, and Killian Clarke for constructive feedback.

1 See, for example, Reference Przeworski and Teune Przeworski and Teune (1970) , Reference Lijphart Lijphart (1971) , Reference Eckstein, Greenstein and Polsby Eckstein (1975) , Reference Yin Yin (1984) , Reference Geddes Geddes (1990) , Reference Collier and Finifter Collier (1993) , Reference Faure Faure (1994) , Reference George and Bennett George and Bennett (2005) , Reference Flyvbjerg Flyvbjerg (2006) , Reference Levy Levy (2008) , Reference Seawright and Gerring Seawright and Gerring (2008) , Reference Gerring Gerring (2007) , Reference Brady and Collier Brady and Collier (2010) , and Reference Tarrow Tarrow (2010) .

2 Some scholars, such as Reference Faure Faure (1994) , distinguish Mill’s dependent-variable driven methods of agreement and difference from the independent-variable driven most-similar and most-different systems designs, suggesting they are distinct. But because, as Figure 7.1 shows, Mill’s dependent-variable driven methods also impose requirements on the array of independent variables to permit causal inference via exclusion, this distinction is not particularly fertile.

3 In Mill’s method of difference, factors present in both cases are eliminated for being insufficient for the outcome (in the method of agreement, factors that vary across the cases are eliminated for being unnecessary).

4 Note that Mill himself distinguished between deductively assessing the average “effect of causes” and inductively retracing the “causes of effects” using the methods of agreement and disagreement ( Reference Mill Mill 1843 [1974] , pp. 449, 764).

5 The proposed approach bears several similarities to Reference Soifer Soifer’s (2020) fertile analysis of how “shadow cases” in comparative research can contribute to theory-building and empirical analysis.

6 This study found that the expansion of clinical services into government facilities embedded in the public health system, the introduction of peer educators, and the harmonization of large quantities of public health data underlay the timing and breadth of the decline in HIV/AIDS amongst female sex workers.

7 What Reference Levy Levy (2008 :13) calls a “deviant” case – which “focus[es] on observed empirical anomalies in existing theoretical propositions” – would also fit within the category of a puzzling case.

8 Process tracing revealed that a conjunction of factors – management turnover and a lackluster culture of staff performance at the state level, inadequate coordination at the federal level, premature disbursement of funds, and citizen aversion to the commercialization of the public water supply – underlay the initially perplexing underperformance of the urban water delivery project.

9 Many thanks to Rory Truex for highlighting this implication of the roadmap in Figure 7.5 .

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• Selecting Cases for Comparative Sequential Analysis
• By Tommaso Pavone
• Edited by Jennifer Widner , Princeton University, New Jersey , Michael Woolcock , Daniel Ortega Nieto
• Book: The Case for Case Studies
• Online publication: 05 May 2022
• Chapter DOI: https://doi.org/10.1017/9781108688253.008

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Research Methods Simplified

Comparative method/quasi-experimental.

• Quantitative Research
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Comparative method or quasi-experimental ---a method used to describe similarities and differences in variables in two or more groups in a natural setting, that is, it resembles an experiment as it uses manipulation but lacks random assignment of individual subjects. Instead it uses existing groups.  For examples see http://www.education.com/reference/article/quasiexperimental-research/#B

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Teleanalysis

Comparative Analysis: Exploring Similarities and Differences in Case Studies

In the realm of research and analysis, comparative studies stand as powerful tools for uncovering insights, patterns, and unique attributes within a diverse range of subjects. By juxtaposing different cases, researchers gain a deeper understanding of the complexities that shape our world. In this article, we’ll dive into the art of comparative analysis, exploring how it sheds light on both similarities and disparities in case danatoto studies.

Understanding Comparative Analysis:

Comparative analysis is a research methodology that involves the systematic examination of two or more cases to discern their similarities and differences. These cases could be countries, organizations, events, individuals, or any other units of analysis.

Why Comparative Analysis Matters:

Approaches to Comparative Analysis:

Key Steps in Conducting Comparative Analysis:

Conclusion:

Comparative analysis stands as a powerful methodology for unraveling the intricacies of diverse cases. By exploring the similarities and differences within and between subjects, researchers gain a deeper understanding of the forces that shape our world. Through thoughtful selection, rigorous analysis, and careful interpretation, comparative studies contribute valuable insights to a wide array of fields.

Narcissistic Personality Disorder: Understanding the Complexities

Terong panggang keju: hidangan lezat dan bergizi yang mudah dibuat, sabun dove global: menyegarkan dunia dengan kelembutan dan perawatan kulit, plopsaland de panne: kombinasi sempurna antara kesenangan dan kenangan indah.

What is Comparative Study

8 Pages Posted: 21 Nov 2011 Last revised: 4 Dec 2011

Syed Aftab Hassan Bukhari

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Date Written: November 20, 2011

Comparative analysis answers questions about how and why a system will react to perturbations of its parameters.This paper shows how perspectives can be used for comparative analysis, summarizes a soundness proof for the technique, demonstrates incompleteness, describes a working implementation, and presents experimental results.

Suggested Citation: Suggested Citation

Syed Aftab Hassan Bukhari (Contact Author)

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Advantages and Disadvantages of Comparative Research Method

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How to Write a Comparative Analysis Dissertation: Useful Guidelines

Writing a dissertation involves more than just demonstrating your expertise in your chosen field of study. It also requires using important skills, such as analytical thinking. Without it, developing sound theories, introducing arguments, or making conclusions would be impossible. And nowhere is this ability more prominently showcased than in writing comparative analysis dissertations.

Comparative analysis is a helpful method you can use to do research. Remember writing compare-and-contrast essays at school? It’s actually very similar to conducting this type of analysis. But it also has plenty of peculiarities that make it a unique approach. Keep reading to learn more about it!

What Is a Comparative Analysis Dissertation?

Comparative analysis types.

• Possible Difficulties
• Elements of Comparative Analysis
• How to Write a Comparative Analysis Dissertation

Comparative analysis boils down to studying similarities and differences between two or more things, be it theories, texts, processes, personalities, or time periods. This method is especially useful in conducting social sciences , humanities, history, and business research.

Conducting a comparative analysis helps you achieve multiple goals:

• It allows you to find parallels and dissimilaritie s between your subjects and use them to make broader conclusions.
• Putting two or more things against each other also helps to see them in a new light and notice the usually neglected aspects.
• In addition to similarities and differences, conducting a comparative analysis helps to determine causality —that is, the reason why these characteristics exist in the first place.

Depending on your research methods, your comparative analysis dissertation can be of two types:

• Qualitative comparative analysis revolves around individual examples. It uses words and concepts to describe the subjects of comparison and make conclusions from them. Essentially, it’s about studying a few examples closely to understand their specific details. This method will be especially helpful if you’re writing a comparative case study dissertation.
• Quantitative comparative dissertations will use numbers and statistics to explain things. It helps make general statements about big sample groups. You will usually need a lot of examples to gather plenty of reliable numerical data for this kind of research.

There are no strict rules regarding these types. You can use the features of both in your comparative dissertation if you want to.

Possible Difficulties of Writing a Comparative Analysis Dissertation

As you can see, comparison is an excellent research method that can be a great help in dissertation writing . But it also has its drawbacks and challenges. It’s essential to be aware of them and do your best to overcome them:

• Your chosen subjects of comparison may have very little in common . In that case, it might be tricky to come up with at least some similarities.
• Sometimes, there may not be enough information about the things you want to study. This will seriously limit your choices and may affect the accuracy of your research results. To avoid it, we recommend you choose subjects you’re already familiar with.
• Choosing a small number of cases or samples will make it much more challenging to generalize your findings . It may also cause you to overlook subtle ways in which the subjects influence each other. That’s why it’s best to choose a moderate number of items from which to draw comparisons, usually between 5 and 40.
• It’s also essential that your dissertation looks different from a s high school compare-and-contrast essay. Instead, your work should be appropriately structured. Read on to learn how to do it!

Elements of Dissertation Comparative Analysis

Do you want your dissertation comparative analysis to be successful? Then make sure it has the following key elements:

• Context Your comparative dissertation doesn’t exist in a vacuum. It has historical and theoretical contexts as well as previous research surrounding it. You can cover these aspects in your introduction and literature review .
• Goals It should be clear to the reader why you want to compare two particular things. That’s why, before you start making your dissertation comparative analysis, you’ll need to explain your goal. For example, the goal of a dissertation in human science can be to describe and classify something.
• Modes of Comparison This refers to the way you want to conduct your research. There are four modes of comparison to choose from: similarity-focused, difference-focused, genus-species relationship, and refocusing.

• Scale This is the degree to which your study will be zooming on the subjects of comparison. It’s similar to looking at maps. There are maps of the entire world, of separate countries, and of smaller locations. The scale of your research refers to how detailed the map is. You will need to use similar scale maps for each subject to conduct a good comparison.
• Scope This criterion refers to how far removed your subjects are in time and space. Depending on the scope, there are two types of comparisons:

• Research Question This is the key inquiry that guides your entire study. In a comparative analysis thesis, the research question usually addresses similarities and differences, but it can also focus on other patterns you’ll be exploring. It can belong to one of the following types, depending on the kind of analysis you want to apply:

Want to write your research question quickly and easily? Try our thesis statement generator ! It has four modes depending on your type of writing, which helps it produce customized results.

• Data Analysis Here, you analyze similarities, differences, and relationships you’ve identified between the subjects. Make sure to provide your argumentation and explain where your findings come from.
• Conclusions This element addresses the research question and answers it. It can also point out the significance of similarities and differences that you’ve found.

How to Write a Comparative Analysis Dissertation

Now that you know what your comparative analysis should include, it’s time to learn how to write it! Follow the steps, and you’ll be sure to succeed:

• Select the Subjects This is the most critical step on which your entire dissertation will depend. To choose things to compare, try to analyze several important factors, including your potential audience , the overall goal of the study, and your interests. It’s also essential to check whether the things you want to discuss are sufficiently studied. While you research possible topics, you may stumble upon untrustworthy AI-generated content. Unfortunately, it’s getting increasingly difficult to differentiate it from human-made writing. To avoid getting into this trap, consider using an AI detection tool . It provides 100% accurate results and is completely free.
• Describe Your Chosen Items Before you can start comparing the subjects, it’s necessary to describe them in their social and historical contexts. Without taking a long, hard look at your topic’s background, it would be impossible to determine what you should pay attention to during your research. To describe your subjects properly, you will need to study plenty of sources and convey their content in your dissertation. Want to simplify this task? Check out our excellent free summarizer tool !
• Juxtapose Now, it’s time to do the comparison by checking how similar and different your subjects are. Some may think focusing on the resemblances is more critical, while others find contrasts more exciting. Both these viewpoints are valid, but the best approach is to find the right balance depending on your study’s goal.
• Provide Redescription Unlike previous steps, this one is optional. It involves looking at something for the second time after conducting the comparison. The point is that you might learn new things about your subjects during your study. They may even help shed light on each other (it’s called “ reciprocal illumination .”) This knowledge will likely deepen your understanding or even change it altogether. It’s a good idea to point it out in your comparative case study dissertation.
• Consider Rectification and Theory Formation These two processes are also optional. They involve upgrading your writing and theories after conducting your research. This doesn’t mean changing the topic of you study. Instead, it refers to changing how you think about your subjects. For example, you may gain some new understanding and realize that you weren’t using the right words to properly describe your subjects. That’s when rectification comes into play. Essentially, you revise the language used in your discussion to make it more precise and appropriate. This new perspective may even inspire you to come up with a new theory about your topic! In that case, you may write about it, too. Usually, though, rectification is enough. If you decide to do it, feel free to use our paraphrasing tool to help you find the right words.
• Edit and Proofread After you’re done writing the bulk of your text, it’s essential to check it and ensure it passes the plagiarism check. After all, even if you haven’t directly copied other people’s texts, there may still be some percentage of accidental plagiarism that can get you in trouble. To ensure that it doesn’t happen, use our free plagiarism detector .

And this is how you write a comparative analysis dissertation! We hope our tips will be helpful to you. Read our next article if you need help with a  literature review in a dissertation . Good luck with your studies!

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Comparative Research

Ai generator.

Although not everyone would agree, comparing is not always bad. Comparing things can also give you a handful of benefits. For instance, there are times in our life where we feel lost. You may not be getting the job that you want or have the sexy body that you have been aiming for a long time now. Then, you happen to cross path with an old friend of yours, who happened to get the job that you always wanted. This scenario may put your self-esteem down, knowing that this friend got what you want, while you didn’t. Or you can choose to look at your friend as an example that your desire is actually attainable. Come up with a plan to achieve your  personal development goal . Perhaps, ask for tips from this person or from the people who inspire you. According to the article posted in  brit.co , licensed master social worker and therapist Kimberly Hershenson said that comparing yourself to someone successful can be an excellent self-motivation to work on your goals.

Aside from self-improvement, as a researcher, you should know that comparison is an essential method in scientific studies, such as experimental research and descriptive research . Through this method, you can uncover the relationship between two or more variables of your project in the form of comparative analysis .

What is Comparative Research?

Aiming to compare two or more variables of an experiment project, experts usually apply comparative research examples in social sciences to compare countries and cultures across a particular area or the entire world. Despite its proven effectiveness, you should keep it in mind that some states have different disciplines in sharing data. Thus, it would help if you consider the affecting factors in gathering specific information.

Quantitative and Qualitative Research Methods in Comparative Studies

In comparing variables, the statistical and mathematical data collection, and analysis that quantitative research methodology naturally uses to uncover the correlational connection of the variables, can be essential. Additionally, since quantitative research requires a specific research question, this method can help you can quickly come up with one particular comparative research question.

The goal of comparative research is drawing a solution out of the similarities and differences between the focused variables. Through non-experimental or qualitative research , you can include this type of research method in your comparative research design.

13+ Comparative Research Examples

Know more about comparative research by going over the following examples. You can download these zipped documents in PDF and MS Word formats.

1. Comparative Research Report Template

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4. Comparative Research Strategies Example

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7. Comparative Area Research Example

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10. Comparative Research in Medical Treatments Example

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14. Casual Comparative Research in DOC

Best Practices in Writing an Essay for Comparative Research in Visual Arts

If you are going to write an essay for a comparative research examples paper, this section is for you. You must know that there are inevitable mistakes that students do in essay writing . To avoid those mistakes, follow the following pointers.

1. Compare the Artworks Not the Artists

One of the mistakes that students do when writing a comparative essay is comparing the artists instead of artworks. Unless your instructor asked you to write a biographical essay, focus your writing on the works of the artists that you choose.

2. Consult to Your Instructor

There is broad coverage of information that you can find on the internet for your project. Some students, however, prefer choosing the images randomly. In doing so, you may not create a successful comparative study. Therefore, we recommend you to discuss your selections with your teacher.

3. Avoid Redundancy

It is common for the students to repeat the ideas that they have listed in the comparison part. Keep it in mind that the spaces for this activity have limitations. Thus, it is crucial to reserve each space for more thoroughly debated ideas.

4. Be Minimal

Unless instructed, it would be practical if you only include a few items(artworks). In this way, you can focus on developing well-argued information for your study.

5. Master the Assessment Method and the Goals of the Project

We get it. You are doing this project because your instructor told you so. However, you can make your study more valuable by understanding the goals of doing the project. Know how you can apply this new learning. You should also know the criteria that your teachers use to assess your output. It will give you a chance to maximize the grade that you can get from this project.

Comparing things is one way to know what to improve in various aspects. Whether you are aiming to attain a personal goal or attempting to find a solution to a certain task, you can accomplish it by knowing how to conduct a comparative study. Use this content as a tool to expand your knowledge about this research methodology .

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Analysis template bundle, 5 steps to make a comparative analysis, step 1: research on the main object, step 2: identify the comparing objects, step 3: note the similarities and differences, step 4: evaluate the findings, step 5: make the decision, 15+ comparative analysis templates, 1. comparative research analysis template, 2. comparative market analysis design template, 3. comparative analysis of safety and security, 4. free comparative analysis of student project work, 5. free comparative analysis essay report example, 6. advertising text qualitative comparative analysis, 7. research comparative analysis example, 8. free comparative competitor analysis document, 9. free qualitative comparative analysis outline, 10. free qualitative comparative analysis study, 11. comparative analysis of system website logs, 12. qualitative comparative analysis comparison chart, 13. bakery restaurant comparative analysis, 14. pavement comparative analysis technical report, 15. free comparative analysis table template, 16. coffee shop comparative analysis, analysis templates.

Comparative Sample Analysis can be any detailed research study or any simple decision on anything that you arrive at by having compared two or more objects. This study is often conducted to have clarity on any subject or to make a decision and avoid confusion. We have designed several templates for comparative Needs Analysis for your convenience, so check those templates out today. You’ll find Sample Outline for a coffee shop, advertising text, Website Design , bakery competitor, Technical Report , restaurant table, and more!

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Comparative analysis of stroke, marital intimacy, marital satisfaction and divorce intention according to the type of participation in marital leisure sports activities.

1. Introduction

Literature review, 2. materials and methods, 2.1. study participants and data collection, 2.2. instruments, 2.3. data analysis, 3.1. validity and reliability, 3.2. multivariate analysis of variance for the comparative analysis, 4. discussion, 5. conclusions and future research, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Yang, J.-H.; Yang, H.J.; Jung, S.C.; Choi, C.; Bum, C.-H. Comparative Analysis of Stroke, Marital Intimacy, Marital Satisfaction and Divorce Intention According to the Type of Participation in Marital Leisure Sports Activities. Behav. Sci. 2024 , 14 , 757. https://doi.org/10.3390/bs14090757

Yang J-H, Yang HJ, Jung SC, Choi C, Bum C-H. Comparative Analysis of Stroke, Marital Intimacy, Marital Satisfaction and Divorce Intention According to the Type of Participation in Marital Leisure Sports Activities. Behavioral Sciences . 2024; 14(9):757. https://doi.org/10.3390/bs14090757

Yang, Ji-Hye, Hye Jin Yang, Si Cheol Jung, Chulhwan Choi, and Chul-Ho Bum. 2024. "Comparative Analysis of Stroke, Marital Intimacy, Marital Satisfaction and Divorce Intention According to the Type of Participation in Marital Leisure Sports Activities" Behavioral Sciences 14, no. 9: 757. https://doi.org/10.3390/bs14090757

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• Published: 24 August 2024

Mixed effects models but not t-tests or linear regression detect progression of apathy in Parkinson’s disease over seven years in a cohort: a comparative analysis

• Anne-Marie Hanff 1 , 2 , 3 , 4 ,
• Rejko Krüger 1 , 2 , 5 ,
• Christopher McCrum 4 ,
• Christophe Ley 6 on behalf of

BMC Medical Research Methodology volume  24 , Article number:  183 ( 2024 ) Cite this article

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Introduction

While there is an interest in defining longitudinal change in people with chronic illness like Parkinson’s disease (PD), statistical analysis of longitudinal data is not straightforward for clinical researchers. Here, we aim to demonstrate how the choice of statistical method may influence research outcomes, (e.g., progression in apathy), specifically the size of longitudinal effect estimates, in a cohort.

In this retrospective longitudinal analysis of 802 people with typical Parkinson’s disease in the Luxembourg Parkinson's study, we compared the mean apathy scores at visit 1 and visit 8 by means of the paired two-sided t-test. Additionally, we analysed the relationship between the visit numbers and the apathy score using linear regression and longitudinal two-level mixed effects models.

Mixed effects models were the only method able to detect progression of apathy over time. While the effects estimated for the group comparison and the linear regression were smaller with high p -values (+ 1.016/ 7 years, p  = 0.107, -0.056/ 7 years, p  = 0.897, respectively), effect estimates for the mixed effects models were positive with a very small p -value, indicating a significant increase in apathy symptoms by + 2.345/ 7 years ( p  < 0.001).

The inappropriate use of paired t-tests and linear regression to analyse longitudinal data can lead to underpowered analyses and an underestimation of longitudinal change. While mixed effects models are not without limitations and need to be altered to model the time sequence between the exposure and the outcome, they are worth considering for longitudinal data analyses. In case this is not possible, limitations of the analytical approach need to be discussed and taken into account in the interpretation.

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In longitudinal studies: “an outcome is repeatedly measured, i.e., the outcome variable is measured in the same subject on several occasions.” [ 1 ]. When assessing the same individuals over time, the different data points are likely to be more similar to each other than measurements taken from other individuals. Consequently, the application of special statistical techniques is required, which take into account the fact that the repeated observations of each subject are correlated [ 1 ]. Parkinson’s disease (PD) is a heterogeneous neurodegenerative disorder resulting in a wide variety of motor and non-motor symptoms including apathy, defined as a disorder of motivation, characterised by reduced goal-directed behaviour and cognitive activity and blunted affect [ 2 ]. Apathy increases over time in people with PD [ 3 ]. Specifically, apathy has been associated with the progressive denervation of ascending dopaminergic pathways in PD [ 4 , 5 ] leading to dysfunctions of circuits implicated in reward-related learning [ 5 ].

T-tests are often misused to analyse changes over time [ 6 ]. Consequently, we aim to demonstrate how the choice of statistical method may influence research outcomes, specifically the size and interpretation of longitudinal effect estimates in a cohort. Thus, the findings are intended for illustrative and educational purposes related to the statistical methodology. In a retrospective analysis of data from the Luxembourg Parkinson's study, a nation-wide, monocentric, observational, longitudinal-prospective dynamic cohort [ 7 , 8 ], we assess change in apathy using three different statistical approaches (paired t-test, linear regression, mixed effects model). We defined the following target estimand: In people diagnosed with PD, what is the change in the apathy score from visit 1 to visit 8? To estimate this change, we formulated the statistical hypothesis as follows:

While apathy was the dependent variable, we included the visit number as an independent variable (linear regression, mixed effects model) and as a grouping variable (paired t-test). The outcome apathy was measured by the discrete score from the Starkstein apathy scale (0 – 42, higher = worse) [ 9 ], a scale recommended by the Movement Disorders Society [ 10 ]. This data was obtained from the National Centre of Excellence in Research on Parkinson's disease (NCER-PD). The establishment of data collection standards, completion of the questionnaires at home at the participants’ convenience, mobile recruitment team for follow-up visits or standardized telephone questionnaire with a reduced assessment were part of the efforts in the primary study to address potential sources of bias [ 7 , 8 ]. Ethical approval was provided by the National Ethics Board (CNER Ref: 201,407/13). We used data from up to eight visits, which were performed annually between 2015 and 2023. Among the participants are people with typical PD and PD dementia (PDD), living mostly at home in Luxembourg and the Greater Region (geographically close areas of the surrounding countries Belgium, France, and Germany). People with atypical PD were excluded. The sample at the date of data export (2023.06.22) consisted of 802 individuals of which 269 (33.5%) were female. The average number of observations was 3.0. Fig. S1 reports the numbers of individuals at each visit while the characteristics of the participants are described in Table  1 .

As illustrated in the flow diagram (Fig.  1 ), the sample analysed from the paired t-test is highly selective: from the 802 participants at visit 1, the t-test only included 63 participants with data from visit 8. This arises from the fact that, first, we analyse the dataset from a dynamic cohort, i.e., the data at visit 1 were not collected at the same time point. Thus, 568 of the 802 participants joined the study less than eight years before, leading to only 234 participants eligible for the eighth yearly visit. Second, after excluding non-participants at visit 8 due to death ( n  = 41) and other reasons ( n  = 130), only 63 participants at visit 8 were left. To discuss the selective study population of a paired t-test, we compared the characteristics (age, education, age at diagnosis, apathy at visit 1) of the remaining 63 participants at visit 8 (included in the paired t-test) and the 127 non-participants at visit 8 (excluded from the paired t-test) [ 12 ].

Flow diagram of patient recruitment

The paired two-sided t-test compared the mean apathy score at visit 1 with the mean apathy score at the visit 8. We attract the reader’s attention to the fact that this implies a rather small sample size as it includes only those people with data from the first and 8th visit. The linear regression analysed the relationship between the visit number and the apathy score (using the “stats” package [ 13 ]), while we performed longitudinal two-level mixed effects models analysis with a random intercept on subject level, a random slope for visit number and the visit number as fixed effect (using the “lmer”-function of the “lme4”-package [ 14 ]). The latter two approaches use all available data from all visits while the paired t-test does not. We illustrated the analyses in plots with the function “plot_model” of the R package sjPlot [ 15 ]. We conducted data analysis using R version 3.6.3 [ 13 ] and the R syntax for all analyses is provided on the OSF project page ( https://doi.org/ https://doi.org/10.17605/OSF.IO/NF4YB ).

Panel A in Fig.  2 illustrates the means and standard deviations of apathy for all participants at each visit, while the flow-chart (Fig. S1 ) illustrates the number of participants at each stage. On average, we see lower apathy scores at visit 8 compared to visit 1 (higher score = worse). By definition, the paired t-test analyses pairs, and in this case, only participants with complete apathy scores at visit 1 and visit 8 are included, reducing the total analysed sample to 63 pairs of observations. Consequently, the t-test compares mean apathy scores in a subgroup of participants with data at both visits leading to different observations from Panel A, as illustrated and described in Panel B: the apathy score has increased at visit 8, hence symptoms of apathy have worsened. The outcome of the t-test along with the code is given in Table  2 . Interestingly, the effect estimates for the increase in apathy were not statistically significant (+ 1.016 points, 95%CI: -0.225, 2.257, p  = 0.107). A possible reason for this non-significance is a loss of statistical power due to a small sample size included in the paired t-test. To visualise the loss of information between visit 1 and visit 8, we illustrated the complex individual trajectories of the participants in Fig.  3 . Moreover, as described in Table S1 in the supplement, the participants at visit 8 (63/190) analysed in the t-test were inherently significantly different compared to the non-participants at visit 8 (127/190): they were younger, had better education, and most importantly their apathy scores at visit 1 were lower. Consequently, those with the better overall situation kept coming back while this was not the case for those with a worse outcome at visit 1, which explains the observed (non-significant) increase. This may result in a biased estimation of change in apathy when analysed by the compared statistical methods.

Bar charts illustrating apathy scores (means and standard deviations) per visit (Panel A: all participants, Panel B: subgroup analysed in the t-test). The red line indicates the mean apathy at visit 1

Scatterplot illustrating the individual trajectories. The red line indicates the regression line

From the results in Table  2 , we see that the linear regression coefficient, representing change in apathy symptoms per year, is not significantly different from zero, indicating no change over time. One possible explanation is the violation of the assumption of independent observations for linear regressions. On the contrary, the effect estimates for the linear mixed effects models indicated a significant increase in apathy symptoms from visit 1 to visit 8 by + 2.680 points (95%CI: 1.880, 3.472, p  < 0.001). Consequently, mixed effects models were the only method able to detect an increase in apathy symptoms over time and choosing mixed effect models for the analysis of longitudinal data reduces the risk of false negative results. The differences in the effect sizes are also reflected in the regression lines in Panel A and B of Fig.  4 .

Scatterplot illustrating the relationship between visit number and apathy. Apathy measured by a whole number interval scale, jitter applied on x- and y-axis to illustrate the data points (Panel A: Linear regression, Panel B: Linear mixed effects model). The red line indicates the regression line

The effect sizes differed depending on the choice of the statistical method. Thus, the paired t-test and the linear regression resulted in an output that would lead to different interpretations than the mixed effects models. More specifically, compared to the t-test and linear regression (which indicated non-significant changes in apathy of only + 1.016, -0.064 points from visit 1 to visit 8, respectively), the linear mixed effects models found an increase of + 2.680 points from visit 1 to visit 8 on the apathy scale. This increase is more than twice as high as indicated by the t-test and suggests linear mixed models is a more sensitive approach to detect meaningful changes perceived by people with PD over time.

Mixed effects models are a valuable tool in longitudinal data analysis as these models expand upon linear regression models by considering the correlation among repeated measurements within the same individuals through the estimation of a random intercept [ 1 , 16 , 17 ]. Specifically, to account for correlation between observations, linear mixed effects models use random effects to explicitly model the correlation structure, thus removing correlation from the error term. A random slope in addition to a random intercept allows both the rate of change and the mean value to vary by participant, capturing individual differences. This distinguishes them from group comparisons or standard linear regressions, in which such explicit modelling of correlation is not possible. Thus, the linear regression not considering correlation among the repeated observations leads to an underestimation of longitudinal change, explaining the smaller effect sizes and insignificant results of the regression. By including random effects, linear mixed effects models can better capture the variability within the data.

Another common challenge in longitudinal studies is missing data. Compared to the paired t-test and regression, the mixed effects models can also include participants with missing data at single visits and account for the individual trajectories of each participant as illustrated in Fig.  2 [ 18 ]. Although multiple imputation could increase the sample size, those results need to be interpreted with caution in case the data is not missing at random [ 18 , 19 ]. Note that we do not further elaborate here on this topic since this is a separate issue to statistical method comparison. Finally, assumptions of the different statistical methods need to be respected. The paired t-test assumes a normal distribution, homogeneity of variance and pairs of the same individuals in both groups [ 20 , 21 ]. While mixed effects models don’t rely on independent observations as it is the case for linear regression, all other assumptions for standard linear regression analysis (e.g., linearity, homoscedasticity, no multicollinearity) also hold for mixed effects model analyses. Thus, additional steps, e.g., check for linearity of the relationships or data transformations are required before the analysis of clinical research questions [ 17 ].

While mixed effects models are not without limitations and need to be altered to model the time sequence between the exposure and the outcome [ 1 ], they are worth considering for longitudinal data analyses. Thus, assuming an increase of apathy over time [ 3 ], mixed effects models were the only method able to detect statistically significant changes in the defined estimand, i.e., the change in apathy from visit 1 to visit 8. Possible reasons are a loss of statistical power due to a small sample size included in the paired t-test and the violence of the assumption of independent observations for linear regressions. Specifically, the effects estimated for the group comparison and the linear regression were smaller with high p -values, indicating a statistically insignificant change in apathy over time. The effect estimates for the mixed effects models were positive with a very small p -value, indicating a statistically significant increase in apathy symptoms from visit 1 to visit 8 in line with clinical expectations. Mixed effects models can be used to estimate different types of longitudinal effects while an inappropriate use of paired t-tests and linear regression to analyse longitudinal data can lead to underpowered analyses and an underestimation of longitudinal change and thus clinical significance. Therefore, researchers should more often consider mixed effects models for longitudinal analyses. In case this is not possible, limitations of the analytical approach need to be discussed and taken into account in the interpretation.

Availability of data and materials

The LUXPARK database used in this study was obtained from the National Centre of Excellence in Research on Parkinson’s disease (NCER-PD). NCER-PD database are not publicly available as they are linked to the Luxembourg Parkinson’s study and its internal regulations. The NCER-PD Consortium is willing to share its available data. Its access policy was devised based on the study ethics documents, including the informed consent form approved by the national ethics committee. Requests for access to datasets should be directed to the Data and Sample Access Committee by email at [email protected].

The code is available on OSF ( https://doi.org/10.17605/OSF.IO/NF4YB )

Abbreviations

Parkinson's disease

Null hypothesis

Alternative hypothesis

Parkinson's disease dementia

National Centre of Excellence in Research on Parkinson's disease

Open Science Framework

Confidence Interval

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Acknowledgements

We would like to thank all participants of the Luxembourg Parkinson’s Study for their important support of our research. Furthermore, we acknowledge the joint effort of the National Centre of Excellence in Research on Parkinson’s Disease (NCER-PD) Consortium members from the partner institutions Luxembourg Centre for Systems Biomedicine, Luxembourg Institute of Health, Centre Hospitalier de Luxembourg, and Laboratoire National de Santé generally contributing to the Luxembourg Parkinson’s Study as listed below:

Geeta ACHARYA 2, Gloria AGUAYO 2, Myriam ALEXANDRE 2, Muhammad ALI 1, Wim AMMERLANN 2, Giuseppe ARENA 1, Michele BASSIS 1, Roxane BATUTU 3, Katy BEAUMONT 2, Sibylle BÉCHET 3, Guy BERCHEM 3, Alexandre BISDORFF 5, Ibrahim BOUSSAAD 1, David BOUVIER 4, Lorieza CASTILLO 2, Gessica CONTESOTTO 2, Nancy DE BREMAEKER 3, Brian DEWITT 2, Nico DIEDERICH 3, Rene DONDELINGER 5, Nancy E. RAMIA 1, Angelo Ferrari 2, Katrin FRAUENKNECHT 4, Joëlle FRITZ 2, Carlos GAMIO 2, Manon GANTENBEIN 2, Piotr GAWRON 1, Laura Georges 2, Soumyabrata GHOSH 1, Marijus GIRAITIS 2,3, Enrico GLAAB 1, Martine GOERGEN 3, Elisa GÓMEZ DE LOPE 1, Jérôme GRAAS 2, Mariella GRAZIANO 7, Valentin GROUES 1, Anne GRÜNEWALD 1, Gaël HAMMOT 2, Anne-Marie HANFF 2, 10, 11, Linda HANSEN 3, Michael HENEKA 1, Estelle HENRY 2, Margaux Henry 2, Sylvia HERBRINK 3, Sascha HERZINGER 1, Alexander HUNDT 2, Nadine JACOBY 8, Sonja JÓNSDÓTTIR 2,3, Jochen KLUCKEN 1,2,3, Olga KOFANOVA 2, Rejko KRÜGER 1,2,3, Pauline LAMBERT 2, Zied LANDOULSI 1, Roseline LENTZ 6, Laura LONGHINO 3, Ana Festas Lopes 2, Victoria LORENTZ 2, Tainá M. MARQUES 2, Guilherme MARQUES 2, Patricia MARTINS CONDE 1, Patrick MAY 1, Deborah MCINTYRE 2, Chouaib MEDIOUNI 2, Francoise MEISCH 1, Alexia MENDIBIDE 2, Myriam MENSTER 2, Maura MINELLI 2, Michel MITTELBRONN 1, 2, 4, 10, 12, 13, Saïda MTIMET 2, Maeva Munsch 2, Romain NATI 3, Ulf NEHRBASS 2, Sarah NICKELS 1, Beatrice NICOLAI 3, Jean-Paul NICOLAY 9, Fozia NOOR 2, Clarissa P. C. GOMES 1, Sinthuja PACHCHEK 1, Claire PAULY 2,3, Laure PAULY 2, 10, Lukas PAVELKA 2,3, Magali PERQUIN 2, Achilleas PEXARAS 2, Armin RAUSCHENBERGER 1, Rajesh RAWAL 1, Dheeraj REDDY BOBBILI 1, Lucie REMARK 2, Ilsé Richard 2, Olivia ROLAND 2, Kirsten ROOMP 1, Eduardo ROSALES 2, Stefano SAPIENZA 1, Venkata SATAGOPAM 1, Sabine SCHMITZ 1, Reinhard SCHNEIDER 1, Jens SCHWAMBORN 1, Raquel SEVERINO 2, Amir SHARIFY 2, Ruxandra SOARE 1, Ekaterina SOBOLEVA 1,3, Kate SOKOLOWSKA 2, Maud Theresine 2, Hermann THIEN 2, Elodie THIRY 3, Rebecca TING JIIN LOO 1, Johanna TROUET 2, Olena TSURKALENKO 2, Michel VAILLANT 2, Carlos VEGA 2, Liliana VILAS BOAS 3, Paul WILMES 1, Evi WOLLSCHEID-LENGELING 1, Gelani ZELIMKHANOV 2,3

1 Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg

2 Luxembourg Institute of Health, Strassen, Luxembourg

3 Centre Hospitalier de Luxembourg, Strassen, Luxembourg

4 Laboratoire National de Santé, Dudelange, Luxembourg

5 Centre Hospitalier Emile Mayrisch, Esch-sur-Alzette, Luxembourg

6 Parkinson Luxembourg Association, Leudelange, Luxembourg

7 Association of Physiotherapists in Parkinson's Disease Europe, Esch-sur-Alzette, Luxembourg

8 Private practice, Ettelbruck, Luxembourg

9 Private practice, Luxembourg, Luxembourg

10 Faculty of Science, Technology and Medicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg

11 Department of Epidemiology, CAPHRI School for Public Health and Primary Care, Maastricht University Medical Centre+, Maastricht, the Netherlands

12 Luxembourg Center of Neuropathology, Dudelange, Luxembourg

13 Department of Life Sciences and Medicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg

This work was supported by grants from the Luxembourg National Research Fund (FNR) within the National Centre of Excellence in Research on Parkinson's disease [NCERPD(FNR/NCER13/BM/11264123)]. The funding body played no role in the design of the study and collection, analysis, interpretation of data, and in writing the manuscript.

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Transversal Translational Medicine, Luxembourg Institute of Health, Strassen, Luxembourg

Anne-Marie Hanff & Rejko Krüger

Translational Neurosciences, Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-Sur-Alzette, Luxembourg

Department of Epidemiology, CAPHRI Care and Public Health Research Institute, Maastricht University Medical Centre+, Maastricht, The Netherlands

Anne-Marie Hanff

Department of Nutrition and Movement Sciences, NUTRIM School of Nutrition and Translational Research in Metabolism, Maastricht University Medical Centre+, Maastricht, The Netherlands

Anne-Marie Hanff & Christopher McCrum

Parkinson Research Clinic, Centre Hospitalier du Luxembourg, Luxembourg, Luxembourg

Rejko Krüger

Department of Mathematics, University of Luxembourg, Esch-Sur-Alzette, Luxembourg

Christophe Ley

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Hanff, AM., Krüger, R., McCrum, C. et al. Mixed effects models but not t-tests or linear regression detect progression of apathy in Parkinson’s disease over seven years in a cohort: a comparative analysis. BMC Med Res Methodol 24 , 183 (2024). https://doi.org/10.1186/s12874-024-02301-7

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The diagnosis performance of [ 18 F]FDG PET/CT, MRI, and CT in the diagnosis of mandibular invasion in oral/oropharyngeal carcinoma: a head-to-head comparative meta-analysis

• Published: 26 August 2024

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This research synthesis investigates the diagnostic performance of [ 18 F]FDG PET/CT, MRI, and CT in detecting mandibular invasion in patients with oral and oropharyngeal cancer.

An extensive literature review was conducted using PubMed and Embase, targeting studies up to March 2024 that examined the diagnostic capabilities of [ 18 F]FDG PET/CT, MRI, and CT for oral and oropharyngeal cancer patients. Sensitivity and specificity were calculated using the DerSimonian and Laird random-effects model with adjustments via the Freeman-Tukey double arc sine transformation. Study quality was assessed with the QUADAS-2 tool.

This meta-analysis synthesized data from 24 studies involving 1376 participants to compare the diagnostic performance of CT, MRI, and [ 18 F]FDG PET/CT for mandibular invasion in oral and oropharyngeal cancer patients. The results showed closely matched sensitivity and specificity among the technologies: CT pooled a sensitivity of 0.80 and specificity of 0.85, while MRI exhibited a slightly better sensitivity at 0.87 but lower specificity at 0.81, with the differences not reaching statistical significance (all P  > 0.05). [ 18 F]FDG PET/CT also demonstrated comparable performance, achieving a sensitivity of 0.77 versus CT’s 0.72 and a specificity of 0.82 versus CT’s 0.93, alongside matching MRI’s sensitivity at 0.86 and a specificity of 0.68 versus MRI’s 0.75, with all comparisons showing no significant disparities (all P  > 0.05).

Conclusions

The meta-analysis concludes that there was no statistically significant difference in diagnostic performance between [ 18 F]FDG PET/CT, CT and MRI. Further research with prospective comparative trials is recommended to validate these findings in new clinical cohorts.

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Zhao, S., Li, X. The diagnosis performance of [ 18 F]FDG PET/CT, MRI, and CT in the diagnosis of mandibular invasion in oral/oropharyngeal carcinoma: a head-to-head comparative meta-analysis. Clin Transl Imaging (2024). https://doi.org/10.1007/s40336-024-00657-w

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Comparative oral monotherapy of psilocybin, lysergic acid diethylamide, 3,4-methylenedioxymethamphetamine, ayahuasca, and escitalopram for depressive symptoms: systematic review and Bayesian network meta-analysis

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• Tien-Wei Hsu , doctoral researcher 1 2 3 ,
• Chia-Kuang Tsai , associate professor 4 ,
• Yu-Chen Kao , associate professor 5 6 ,
• Trevor Thompson , professor 7 ,
• Andre F Carvalho , professor 8 ,
• Fu-Chi Yang , professor 4 ,
• Ping-Tao Tseng , assistant professor 9 10 11 12 ,
• Chih-Wei Hsu , assistant professor 13 ,
• Chia-Ling Yu , clinical pharmacist 14 ,
• Yu-Kang Tu , professor 15 16 ,
• 1 Department of Psychiatry, E-DA Dachang Hospital, I-Shou University, Kaohsiung, Taiwan
• 2 Department of Psychiatry, E-DA Hospital, I-Shou University, Kaohsiung, Taiwan
• 3 Graduate Institute of Clinical Medicine, College of Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan
• 4 Department of Neurology, Tri-Service General Hospital, National Defense Medical Centre, Taipei, Taiwan
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• Accepted 20 June 2024

Objective To evaluate the comparative effectiveness and acceptability of oral monotherapy using psychedelics and escitalopram in patients with depressive symptoms, considering the potential for overestimated effectiveness due to unsuccessful blinding.

Design Systematic review and Bayesian network meta-analysis.

Data sources Medline, Cochrane Central Register of Controlled Trials, Embase, PsycINFO, ClinicalTrial.gov, and World Health Organization’s International Clinical Trials Registry Platform from database inception to 12 October 2023.

Eligibility criteria for selecting studies Randomised controlled trials on psychedelics or escitalopram in adults with depressive symptoms. Eligible randomised controlled trials of psychedelics (3,4-methylenedioxymethamphetamine (known as MDMA), lysergic acid diethylamide (known as LSD), psilocybin, or ayahuasca) required oral monotherapy with no concomitant use of antidepressants.

Data extraction and synthesis The primary outcome was change in depression, measured by the 17-item Hamilton depression rating scale. The secondary outcomes were all cause discontinuation and severe adverse events. Severe adverse events were those resulting in any of a list of negative health outcomes including, death, admission to hospital, significant or persistent incapacity, congenital birth defect or abnormality, and suicide attempt. Data were pooled using a random effects model within a Bayesian framework. To avoid estimation bias, placebo responses were distinguished between psychedelic and antidepressant trials.

Results Placebo response in psychedelic trials was lower than that in antidepression trials of escitalopram (mean difference −3.90 (95% credible interval −7.10 to −0.96)). Although most psychedelics were better than placebo in psychedelic trials, only high dose psilocybin was better than placebo in antidepression trials of escitalopram (mean difference 6.45 (3.19 to 9.41)). However, the effect size (standardised mean difference) of high dose psilocybin decreased from large (0.88) to small (0.31) when the reference arm changed from placebo response in the psychedelic trials to antidepressant trials. The relative effect of high dose psilocybin was larger than escitalopram at 10 mg (4.66 (95% credible interval 1.36 to 7.74)) and 20 mg (4.69 (1.64 to 7.54)). None of the interventions was associated with higher all cause discontinuation or severe adverse events than the placebo.

Conclusions Of the available psychedelic treatments for depressive symptoms, patients treated with high dose psilocybin showed better responses than those treated with placebo in the antidepressant trials, but the effect size was small.

Systematic review registration PROSPERO, CRD42023469014.

Introduction

Common psychedelics belong to two classes: classic psychedelics, such as psilocybin, lysergic acid diethylamide (known as LSD), and ayahuasca; and entactogens, such as 3,4-methylenedioxymethamphetamine (MDMA). 1 Several randomised controlled trials have shown efficacy of psychedelics for people with clinical depression. 2 3 The proposed mechanism of its fast and persistent antidepressant effects is to promote structural and functional neuroplasticity through the activation of intracellular 5-HT 2A receptors in the cortical neurons. 4 Additionally, the increased neuroplasticity was associated with psychedelic’s high affinity directly binding to brain derived neurotrophic factor receptor TrkB, indicating a dissociation between the hallucinogenic and plasticity promoting effects of psychedelics. 5 A meta-analysis published in 2023 reported that the standardised mean difference of psychedelics for depression reduction ranged from 1.37 to 3.12, 2 which are considered large effect sizes. 6 Notably, the standardised mean difference of antidepressant trials is approximately 0.3 (a small effect size). 7 8

Although modern randomised controlled trials involving psychedelics usually use a double blinded design, the subjective effects of these substances can compromise blinding. 9 Unsuccessful blinding may lead to differing placebo effects between the active and control groups, potentially introducing bias into the estimation of relative treatment effects. 10 Concerns have arisen regarding the overestimated effect sizes of psychedelics due to the issues of blinding and response expectancy. 9 Psychedelic treatment is usually administered with psychological support or psychotherapy, and thereby the isolated pharmacological effects of psychedelics remain to be determined. 2 Surprisingly, on 1 July 2023, Australia approved psilocybin for the treatment of depression 11 ; the first country to classify psychedelics as a medicine at a national level.

To date, only one double blind, head-to-head randomised controlled trial has directly compared a psychedelic drug (psilocybin) with an antidepressant drug (escitalopram) for patients with major depressive disorder. 12 This randomised controlled trial reported that psilocybin showed a better efficacy than escitalopram on the 17 item Hamilton depression rating scale (HAMD-17).

We aimed to assess the comparative effectiveness and acceptability of oral monotherapy with psychedelics and escitalopram in patients experiencing depressive symptoms. Given that unsuccessful blinding can potentially lead to a reduced placebo response in psychedelic trials, we distinguished between the placebo responses in psychedelic and antidepressant trials. We also investigated the differences in patient responses between people who received extremely low dose psychedelics as a placebo and those who received a placebo in the form of a fake pill, such as niacin, in psilocybin trials. 13 14 Our study allowed for a relative effect assessment of psychedelics compared with placebo responses observed in antidepressant trials.

The study protocol was registered with PROSPERO (CRD42023469014). We followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) extension statement for reporting systematic reviews incorporating network meta-analysis (NMA) (appendix 1). 15

Data sources and searches

A comprehensive search of the Medline, Cochrane Central Register of Controlled Trials (CENTRAL), Embase, PsycINFO, ClinicalTrial.gov, and World Health Organization’s International Clinical Trials Registry Platform databases were performed without language restrictions from database inception to 12 October 2023. We also searched the grey literature and reviewed reference lists of the included studies and related systematic reviews. 2 3

Study selection

Eligible studies were randomised controlled trials with parallel group or crossover designs. We included: (i) adults (≥18 years) with clinically diagnosed depression (eg, major depressive disorder, bipolar disorder, or other psychiatric disorders with comorbid clinical depression) or life threatening diagnoses and terminal illness with depressive symptoms; and (ii) adults with assessment of treatment response (preapplication/postapplication) using standard, validated, and internationally recognised instruments, such as HAMD-17. The outcome of interest was the change in depressive symptoms at the end of treatment compared with the controls, and we only extracted data from the first phase of crossover randomised controlled trials to avoid carry-over effects. Eligible psychedelic randomised controlled trials (including psilocybin, lysergic acid diethylamide, MDMA, and ayahuasca without dosage limit) required oral monotherapy without the concomitant use of antidepressants. For escitalopram, we included only fixed dose randomised controlled trials that compared at least two arms with different doses of oral form escitalopram (maximum dose of 20 mg/day) with placebo because psychedelic therapies usually use a fixed dose study design. We also included randomised controlled trials that evaluated psychedelic monotherapy compared with escitalopram monotherapy. We excluded follow-up studies and studies with healthy volunteers. We also excluded conference abstracts, editorials, reviews, meta-analyses, case reports, and case series, as well as publications reporting duplicate data. We did not consider ketamine because this drug is usually administered parenterally and is not a classic psychedelic. 16 Screening and selection of the studies were performed independently by two authors. Discrepancies in study inclusion were resolved by deliberation among the reviewer pairs or with input from a third author. Appendix 2 shows the complete search strategies, and appendix 3 presents the reasons for exclusion.

Definition of outcomes, data extraction, and risk of bias assessment

The primary outcome was change in depressive symptoms from baseline (continuous outcome), as measured by a validated rating scale, such as HAMD-17. When multiple measurement tools were used, they were selected in the following order: the HAMD-17, Montgomery-Åsberg depression rating scale, and Beck depression inventory (second edition). To improve interpretability, all extracted depression scores were converted to corresponding HAMD-17 scores using a validated method. 17 We used a conservative correlation coefficient of 0.5 or other statistics (eg, t statistics) to calculate the standard deviation of change from baseline when unreported. 18 The secondary outcomes were all cause discontinuation and severe adverse events (categorical outcomes). Severe adverse events were classified as those resulting in any of a list of negative health outcomes including, death, admission to hospital, significant or persistent incapacity, congenital birth defect or abnormality, and suicide attempt. Outcome data were extracted from original intention-to-treat or last observation carrying forward analysis, as well as from estimates of mixed-effect models for repeated measures.

Two authors independently extracted and reviewed the data, each being reviewed by another author. WebPlot Digitizer ( https://automeris.io/WebPlotDigitizer/ ) was used to extract numerical data from the figures. Two authors independently used the Cochrane randomised trial risk of bias tool (version 2.0) to assess the risk of bias in the included trials, and discrepancies were resolved by consensus. 19

Data synthesis

To estimate the relative effect between two interventions, we computed mean difference on the basis of change values (with 95% credible interval) for continuous outcomes (change in depressive symptoms) and odds ratios for categorical outcomes (all cause discontinuation and severe adverse event). To assess the clinical significance of the relative effect, we evaluated whether the mean difference exceeded the minimal important difference, which is estimated to be 3 points for HAMD-17. 20 We defined high, low, and extremely low doses of the included psychedelics as follows: (i) psilocybin: high dose (≥20 mg), extremely low dose (1-3 mg), low dose (other range); and (ii) MDMA: high dose (≥100 mg), extremely low dose (≤40 mg), low dose (other range). Escitalopram was divided into escitalopram 10 mg and escitalopram ≥20 mg. In previous clinical trials, a dose of 1 mg of psilocybin or a dose range of 1-3 mg/70 kg were used as an active control because these doses were believed not to produce significant psychedelic effects. 21 22 A dose of 5 mg/70 kg can produce noticeable psychedelic effects. 22 In many two arm psilocybin trials, the psilocybin dose in the active group typically falls within the range of 20-30 mg. 12 21 23 24 In a three arm trial, 25 mg was defined as high dose, and 10 mg was considered a moderate dose. 21 Another clinical trial also defined 0.215 mg/kg of psilocybin as a moderate dose for the active group. 25 Therefore, we used 20 mg and 3 mg as the boundaries for grouping psilocybin doses; when the dosage was calculated per kilogram in the study, we converted it to per 70 kg. For MDMA, in two trials with three arms, 125 mg was defined as high dose, and 30-40 mg was defined as active control. 26 27 Thus, we used 100 mg and 40 mg as the boundaries for grouping MDMA doses.

We conducted random effects network meta-analysis and meta-analysis within a Bayesian framework. 28 29 Previous meta-analyses considered all control groups as a common comparator; however, concerns have been raised regarding the overestimated effect sizes of psychedelics because of unsuccessful blinding and poor placebo response. 9 Therefore, we treated the three treatments as distinct interventions: the placebo response observed in psychedelic trials, the placebo response observed in antidepressant escitalopram trials, and extremely low dose psychedelics (ie, psilocybin and MDMA). We calculated the relative effects of all interventions compared with these three groups, indicating the following three conditions: (1) the treatment response of placebo response in the psychedelic trials is assumed to be lower than that of placebo response in antidepressant trials because of unsuccessful blinding. 9 As such, the relative effects compared with placebo response in the psychedelic trials represented potential overestimated effect sizes. (2) the placebo response in antidepressant trials is assumed to be the placebo response in antidepressant trials with adequate blinding, therefore, the relative effects compared with placebo response in antidepressant trials represents effect sizes in trials with adequate blinding. (3) Psychedelic drugs are usually administered with psychotherapy 13 or psychological support, 14 the relative effects of psychedelics compared with extremely low dose psychedelics might eliminate the concomitant effects from psychotherapeutic support, approximating so-called pure pharmacological effects.

In network meta-analysis, the validity of indirect comparison relies on transitivity assumption. 30 We assessed the transitivity assumption by comparing the distribution of potential effect modifies across treatment comparisons. In addition, we assessed whether the efficacy of escitalopram is similar in placebo controlled randomised controlled trials (escitalopram v placebo response in antidepressant trials) and in the head-to-head randomised controlled trial (psilocybin v escitalopram) using network meta-analysis. 12 Furthermore, we assessed the efficacy of the different placebo responses (placebo response in the psychedelic trials v placebo response in antidepressant trials) as additional proof of transitivity. If the placebo response in antidepressant trials was better than that in the psychedelic trials, the transitivity assumption did not hold when grouping placebo response in antidepressant trials and placebo response in the psychedelic trials together. Finally, for the primary outcome (change in depressive symptoms), network meta-regression analyses were conducted to evaluate the impact of potential effect modifiers, including proportion of men and women in the study, mean age, baseline depression severity, disorder type, and follow-up assessment period. We assumed a common effect on all treatment comparisons for each of the effect modifiers. In other words, all interactions between the treatment comparisons and the effect modifier were constrained to be identical.

We also conducted the following sensitivity analyses: analysing studies of patients with major depressive disorder; excluding studies with a high risk of bias; adjusting for baseline depression severity; and using correlation coefficient of zero (most conservative) to calculate the standard deviation of change from baseline when unreported.

Publication bias was assessed by visual inspection of a comparison adjusted funnel plots. The first funnel plot used placebo response in the psychedelic trials as the comparator. The second funnel plot used placebo response in antidepressant trials as the comparator. The third funnel plot used both placebo response in the psychedelic trials and placebo response in antidepressant trials as comparators simultaneously. Additionally, we conducted the Egger test, Begg test, and Thompson test to examine the asymmetry of the third funnel plot. A previous meta-analysis reported that the standardised mean difference of psychedelics for depression reduction ranged from 1.37 to 3.12. 2 Therefore, we also transformed the effect size of mean difference to standardised mean difference (Hedges’ g) for the primary outcome. The global inconsistency of the network meta-analysis was examined by fitting an unrelated main effects model. Local inconsistency of the network meta-analysis was examined using node splitting methods. 31 Four Markov chains were implemented. 50 000 iterations occurred per chain and the first 20 000 iterations for each chain were discarded as a warm-up. Convergence was assessed by visual inspection of the trace plots of the key parameters for each analysis. The prior settings and convergence results are shown in appendix 4. All statistical analyses were done using R version 4.3.1. The network meta-analysis and pairwise meta-analysis within a Bayesian framework were fitted using the Bayesian statistical software called Stan within the R packages multinma 28 and brms, 29 respectively. The frequentist random effects network meta-analysis, funnel plots, and tests for funnel plot asymmetry were conducted using the R package netmeta. Reasons for protocol changes are in appendix 5.

Assessment certainty of evidence for the primary outcome

The certainty of evidence produced by the network meta-analysis was evaluated using GRADE (Grading of recommendations, assessment, development and evaluation). 32 33 We used a minimally contextualised framework with the value of 3 (minimal important difference) as our decision threshold. The certainty of evidence refers to our certainty that the intervention had, relative to minimal intervention, any clinically minimal important difference. The optimal information size was calculated using a validated method. 32 33 34

Patient and public involvement

Both patients and the public are interested in research on novel depression treatments and their efficacy compared with existing antidepressants. However, due to a scarcity of available funding for recruitment and researcher training, patients and members of the public were not directly involved in the planning or writing of this manuscript. We did speak to patients about the study, and we asked a member of the public to read our manuscript after submission.

Characteristics of included study

After searching the database and excluding duplicated records, we identified 3104 unique potential studies. We then screened the titles and abstracts of these studies for eligibility and excluded 3062 of them, in which 42 studies remained. Twenty six studies were excluded after an assessment of the full text for various reasons (appendix 3). We identified three additional studies through a manual search resulting in total 19 eligible studies (efigure 1). Details of the characteristics of the included studies are shown in etable 1. Protocols of psychological support or psychotherapy with psychedelic treatment are shown in etable 2. Overall, 811 people (mean age of 42.49 years, 54.2% (440/811) were women) were included in psychedelic trials (15 trials), and 1968 participants (mean age of 39.35 years, 62.5% (1230/1968) were women) were included in escitalopram trials (five trials).

Risk of bias of the included studies

No psychedelic study (0/15) had a high overall risk of bias (efigure 2A and efigure 3A). The percentages of studies with high, some concerns, or low risk of bias in the 15 psychedelic trials were as follows: 0% (k=15), 33% (k=5), and 67% (k=10) for randomisation; 0% (k=0), 33% (k=5), and 67% (k=10) for deviations from intended interventions; 0% (k=0), 13% (k=2), and 87% (k=13) for missing outcome data; 0% (k=0), 33% (k=5), and 67% (k=10) for measurements of outcomes; 0% (k=0), 67% (k=1), and 93% (k=14) for selection of reported results. No non-psychedelic studies (0/5) were rated as high risk of bias (efigure 2B and efigure 3B). The percentages of studies with high, some concerns, and low risk of bias in the five non-psychedelic trials were as follows: 0% (k=0), 80% (k=4), and 20% (k=1) for randomisation; 0% (k=0), 100% (k=5), and 0% (k=0) for deviations from intended interventions; 0% (k=0), 80% (k=4), and 20% (k=1) for missing outcome data; 0% (k=0), 80% (k=4), and 20% (k=1) for measurements of outcomes; 0% (k=0), 20% (k=1), and 80% (k=4) for selection of reported results.

Network meta-analysis

In the network structure, all interventions were connected, with two main structures ( fig 1 ). All psychedelics were compared with placebo response in the psychedelic trials, and escitalopram was compared with placebo response in antidepressant trials. A head-to-head comparison of high dose psilocybin and 20 mg escitalopram connected the two main structures. 12

Network structure. LSD=lysergic acid diethylamide; MDMA=3,4-methylenedioxymethamphetamine

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In the main network meta-analysis, all interventions, except for extremely low dose and low dose MDMA, were associated with a larger mean difference exceeding the minimal important difference of 3 points on the HAMD-17 than with placebo response in the psychedelic trials ( fig 2 ). Notably, placebo response in antidepressant trials (3.79 (95% credibile interval 0.77 to 6.80)) and extremely low dose psilocybin (3.96 (0.61 to 7.17)) were better than placebo response in the psychedelic trials, with mean differences exceeding 3 and 95% credibile intervals that did not cross zero. Additionally, in comparison with placebo response in antidepressant trials ( fig 2 ), the relative effects of high dose psilocybin (6.52 (3.19 to 9.57)), escitalopram 10 mg (1.86 (0.21 to 3.50)), and escitalopram 20 mg (1.82 (0.16 to 3.43)) did not cross zero. Only high dose psilocybin resulted in a mean difference that was greater than 3. The standardised mean difference of high dose psilocybin decreased from large (0.88) to small (0.31) when the reference arm was changed from placebo response in the psychedelic trials to placebo response in antidepressant trials.

Forest plots of network meta-analytical estimates v different reference arms by observed placebo response. The dotted line represents the minimal important difference of 3 whereas the red line indicates 0. LSD=lysergic acid diethylamide; MDMA=3,4-methylenedioxymethamphetamine

When compared with extremely low dose psilocybin ( fig 2 ), only the relative effects of high dose psilocybin (6.35 (95% credibile interval 3.41 to 9.21)) and placebo response in the psychedelic trials (−3.96 (−7.17 to −0.61)) showed a larger mean difference exceeding 3, without crossing zero. All relative effects between interventions are showed in efigure 4. Importantly, the mean differences of high dose psilocybin compared with escitalopram 10 mg (4.66 (1.36 to 7.74); standardised mean difference 0.22), escitalopram 20 mg (4.69 (1.64 to 7.54); 0.24), high dose MDMA (4.98 (1.23 to 8.67); 0.32), and low dose psilocybin (4.36 (1.20 to 7.51); 0.32) all exceeded 3 and did not cross zero (efigure 4).

Transitivity assumption

The assessment of transitivity assumption is showed in efigure 5 and efigure 6. We compared the efficacy of escitalopram in the placebo controlled antidepressant trials 8 with that in the head-to-head trial (psilocybin v escitalopram) 12 using network meta-analysis and pairwise meta-analysis. The results of the network meta-analysis showed that the relative effects between these two study designs (0.64 (95% credibile interval −4.41 to 5.40), efigure 6A; 1.94 (−2.66 to 6.14), efigure 6B) included zero, and the mean differences did not exceed 3. Placebo response in antidepressant trials was better than placebo response in the psychedelic trials with a small effect size (3.79 (0.77 to 6.80), standardised mean difference 0.2), and the mean difference exceed 3 ( fig 2 ).

Sensitivity analyses

When including only patients with major depressive disorder, the relative effects of escitalopram 20 mg, escitalopram 10 mg, ayahuasca, and high dose psilocybin were better than placebo response in antidepressant trials, while placebo response in the psychedelic trials was worse than placebo response in antidepressant trials ( fig 3 ). However, only the mean differences for high dose psilocybin (6.82 (95% credibile interval 3.84 to 9.67)), ayahuasca (5.38 (0.02 to 10.61)), and placebo response in the psychedelic trials (−4.00 (−6.87 to −1.13)) exceeded 3. When compared with extremely low dose psilocybin (excluding the effects from concomitant psychotherapeutic support), only the 95% credibile intervals of the relative effects of high dose psilocybin (4.36 (0.54 to 8.27); standardised mean difference 0.30) and placebo response in the psychedelic trials (−6.46 (−10.41 to −2.32), standardised mean difference −0.46) exceeded 3 and did not cross zero ( fig 3 ). All of the relative effects between interventions are showed in efigure 7. Notably, the relative effects of high dose psilocybin compared with escitalopram 10 mg (4.96 (1.97 to 7.82)), escitalopram 20 mg (4.97 (2.19 to 7.64)), and low dose psilocybin (3.82 (0.61 to 7.04)) all exceeded 3 and did not cross zero (efigure 7).

Forest plots of network meta-analytical estimates when considering a population with major depressive disorder

The other three sensitivity analyses showed similar findings with the main analyses: exclusion of studies with high risk of bias (efigure 8); adjustment of baseline depression severity (efigure 9); and use of most conservative correlation coefficient of zero (efigure 10).

All cause discontinuation and severe adverse event

When referencing placebo in psychedelic trials, no interventions were associated with higher risks of all cause discontinuation rate nor severe adverse event rate (efigure 11).

Network meta-regression and publication bias

In network meta-regression analyses, the 95% credibile intervals of the relative effects of the baseline depressive severity, mean age, and percentage of women, crossed zero (etable 3). The results of the statistical tests (Egger, Begg, and Thompson-Sharp tests) for funnel plot asymmetry and visual inspection of funnel plots did not show publication bias (efigure 12). The results of GRADE assessment are provided in the efigure 13. Most of the certainty of evidence for treatment comparisons was moderate or low.

Consistency assumptions

The back calculation methods for all the models (appendix 6) did not show any inconsistencies. The node splitting methods also did not show any inconsistencies (appendix 7).

Principal findings

This network meta-analysis investigated the comparative effectiveness between psychedelics and escitalopram for depressive symptoms. Firstly, we found that the placebo response observed in antidepressant trials was associated with greater effectiveness than that observed in psychedelic trials. Secondly, when compared with placebo responses in antidepressant trials, only escitalopram and high dose psilocybin were associated with greater effectiveness, and only high dose psilocybin exceeded minimal important difference of 3. Notably, the effect size of high dose psilocybin decreased from large to small. Thirdly, among the included psychedelics, only high dose psilocybin was more likely to be better than escitalopram 10 mg or 20 mg, exceeding the minimally important difference of 3. Fourthly, in patients with major depressive disorder, escitalopram, ayahuasca, and high dose psilocybin were associated with greater effectiveness than placebo responses in antidepressant trials; however, only high dose psilocybin was better than extremely low dose psilocybin, exceeding minimal important difference of 3. Taken together, our study findings suggest that among psychedelic treatments, high dose psilocybin is more likely to reach the minimal important difference for depressive symptoms in studies with adequate blinding design, while the effect size of psilocybin was similar to that of current antidepressant drugs, showing a mean standardised mean difference of 0.3. 7

Comparison with other studies

In a randomised controlled trial, treatment response was defined as the response observed in the active arm; placebo response was defined as the response observed in the control (placebo) arm. 10 Treatment response consists of non-specific effects, placebo effect, and true treatment effect; placebo response consisted of non-specific effects and placebo effect. Therefore, when the placebo effect is not the same for the active and control arms within an randomised controlled trial, the estimation of the true treatment effect is biased. For example, in a psychedelic trial, unsuccessful blinding may occur due to the profound subjective effects of psychedelics. This unblinding may lead to high placebo effect in the active arm and low placebo effect in the control arms, and the true treatment effect is overestimated. 10 Without addressing unequal placebo effects within studies, the estimation of meta-analysis and network meta-analysis are biased. 10 However, in most psychedelic trials, blinding was either reported as unsuccessful or not assessed at all. For example, two trials of lysergic acid diethylamide reported unsuccessful blinding, 35 36 whereas the trial of ayahuasca only reported that five of 10 participants misclassified the placebo as ayahuasca. 37 In trials of MDMA, participants' accuracy in guessing which treatment arm they were in ranged from approximately 60-90%. 26 27 38 39 40 In the case of most psilocybin trials, blinding was not assessed, with the exception of the study by Ross and colleagues in 2016. 13 In that study, participants were asked to guess whether the psilocybin or an active control was received, and the correct guessing rate was 97%. In our study, we established several network meta-analysis models addressing this issue, and we found that placebo response in the psychedelic trials was associated with less effectiveness than that in antidepressant trials. Therefore, the effect sizes of psychedelics compared with placebo response observed in psychedelic trials may be overestimated. All of the psychedelics’ 95% credibile intervals of the relative effects crossed zero when compared with the placebo response in antidepressant trials, except for high dose psilocybin.

The comparisons between psychedelics and escitalopram showed that high dose psilocybin was more likely to be better than escitalopram. Psilocybin was usually administered with psychotherapy or psychological support. 13 14 Therefore, the greater effectiveness of psilocybin may be from not only pharmacological effects but also psychotherapeutic support. However, we also found that high doses of psilocybin was associated greater effectiveness than extremely low doses of psilocybin. This effect also indicates that the effectiveness of psilocybin cannot be attributed only to concomitant psychotherapy or psychological support.

In patients with major depressive disorder, ayahuasca, low dose psilocybin, high dose psilocybin, escitalopram 10 mg, and escitalopram 20 mg were associated with greater effectiveness than the placebo response in antidepressant trials . However, when compared with extremely low dose psilocybin, only high dose psilocybin was associated with better effectiveness; the standardised mean difference decreased from 0.38 (compared with placebo response in antidepressant trials) to 0.30 (compared with extremely low dose psilocybin). As such, the effectiveness of psilocybin should be considered with concomitant psychotherapeutic support in people with major depressive disorder. The effect size of high dose psilocybin was similar with antidepressant trials of patients with major depressive disorder showing a mean standardised mean difference of 0.3. 7 8

Strengths and limitations of this study

This study has several strengths. We conducted separate analyses for placebo response in antidepressant trials, placebo response in psychedelic trials, and an extremely low active dose of psychedelics, thereby mitigating the effect of placebo response variations across different studies. This approach allowed us to assess the efficacy of psychedelics more impartially and make relatively unbiased comparisons than if these groups were not separated. This study supported the transitivity assumption of the efficacy of escitalopram in placebo controlled antidepressant trials with that in psilocybin versus escitalopram head-to-head trial, thereby bridging the escitalopram trials and psychedelic trials. We also performed various sensitivity analyses to ensure the validation of our statistical results.

Nevertheless, our study has several limitations. Firstly, we extracted only the acute effects of the interventions. A comparison of the long term effects of psychedelics and escitalopram remains unclear. Secondly, participants in the randomised controlled trials on MDMA were predominantly diagnosed with post-traumatic stress disorder, whereas participants in the randomised controlled trials on escitalopram were patients with major depressive disorder. However, depressive symptoms in post-traumatic stress disorder could be relatively treatment resistant, requiring high doses of psychotropic drugs. 41 Moreover, our study focused not only on major depressive disorder but also on the generalisability of psychedelic treatment for depressive symptoms. Thirdly, although all available studies were included, the sample size of the psychedelic randomised controlled trials was small (k=15). Fourthly, when using extremely low dose psychedelics as a reference group, the relative effect may also eliminate some pharmacological effects because our study found that extremely low dose psychedelics could not be considered a placebo. Fifthly, in network meta-analysis, direct evidence for one treatment comparison may serve as indirect evidence for other treatment comparisons, 42 and biases in the direct evidence might affect estimates of other treatment comparisons. Because the absolute effect of escitalopram in the head-to-head trial (high dose psilocybin v escitalopram 20 mg) 12 was lower than those of placebo controlled trials, the relative effects of high dose psilocybin might be slightly overestimated when compared with other treatments in the current study. We addressed this issue by use of a Bayesian network meta-analysis, distinguishing between placebo response in psychedelic trials and placebo response in antidepressant trials. Specifically, we only considered that the 95% credibile interval of the relative effect between two comparisons did not cross zero. Indeed, the relative effect of escitalopram 20 mg between these two study designs included zero. Finally, our network meta-analysis may not have sufficient statistical power to detect potential publication bias due to the scarcity of trials and participants.

Implications and conclusions

Serotonergic psychedelics, especially high dose psilocybin, appeared to have the potential to treat depressive symptoms. However, study designs may have overestimated the efficacy of psychedelics. Our analysis suggested that the standardised mean difference of high dose psilocybin was similar to that of current antidepressant drugs, showing a small effect size. Improved blinding methods and standardised psychotherapies can help researchers to better estimate the efficacy of psychedelics for depressive symptoms and other psychiatric conditions.

What is already known on this topic

Psychedelic treatment resulted in significant efficacy in treating depressive symptoms and alleviating distress related to life threatening diagnoses and terminal illness

Meta-analyses have reported standardised mean difference of psychedelics for depression reduction ranging from 1.37 to 3.12, while antidepressant trials were approximately 0.3

No network meta-analysis has examined comparative efficacy between psychedelics and antidepressants for depressive symptoms, and effect sizes of psychedelics might be overestimated because of unsuccessful blinding and response expectancies

What this study adds

To avoid estimation bias, placebo responses in psychedelic and antidepressant trials were separated; placebo response in psychedelic trials was lower than that in antidepressant trials

Among all psychedelics studied, only high dose psilocybin was associated with greater effectiveness than placebo response in antidepressant trials (standardised mean difference 0.31)

Among all psychedelics, only high dose psilocybin was associated with greater effectiveness than escitalopram

Ethics statements

Ethical approval.

Not required because this study is an analysis of aggregated identified clinical trial data.

Data availability statement

The data that support the findings of this study are available from the corresponding author (C-SL) upon reasonable request.

Contributors: T-WH and C-KT contributed equally to this work and are joint first authors. Y-KT and C-SL contributed equally to this work and are joint last/corresponding authors. C-SL, T-WH, and Y-KT conceived and designed the study. T-WH, C-KT, C-WH, and P-TT selected the articles, extracted the data, and assess the risk of bias. C-LY did the systemic search. T-WH and C-SL wrote the first draught of the manuscript. TT, AFC, Y-CK, F-CY, and Y-KT interpreted the data and contributed to the writing of the final version of the manuscript. C-KT and T-WH have accessed and verified the data. C-SL and Y-KT were responsible for the decision to submit the manuscript. All authors confirmed that they had full access to all the data in the study and accept responsibility to submit for publication. The corresponding author attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted.

Funding: The study was supported by grant from the National Science and Technology Council (NSTC 112-2314-B-016−036-MY2 and NSTC 112-2314-B-002−210-MY3). The funding source had no role in any process of our study.

Competing interests: All authors have completed the ICMJE uniform disclosure form at www.icmje.org/disclosure-of-interest/ and declare: support from National Science and Technology Council for the submitted work; no financial relationships with any organisations that might have an interest in the submitted work in the previous three years; no other relationships or activities that could appear to have influenced the submitted work.

Transparency: The lead author (C-SL) affirms that the manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned

Dissemination to participants and related patient and public communities: Dissemination of the work to the public and clinical community through social media and lectures is planned.

Provenance and peer review: Not commissioned; externally peer reviewed.

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http://creativecommons.org/licenses/by/4.0/ .

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1 Introduction

2 literature review, 2.1 tourism utilization of linear cultural heritage, 2.2 spatial-temporal distribution of the tourism industry along linear cultural heritage, 2.3 factors influencing the tourism industry distribution along linear cultural heritage, 2.4 tourism development of the beijing-hangzhou grand canal, 3 methodology, 3.1 study sites, 3.1.1 beijing section, 3.1.2 liaocheng section, 3.1.3 yangzhou section, 3.2 data collection, 3.2.1 tourism industry data, 3.2.2 influencing factors, 3.3 data analysis, 3.3.1 nearest neighbor analysis, 3.3.2 kernel density estimation, 3.3.3 standard deviational ellipse, 3.3.4 geo-detector, 4.1 spatial-temporal distribution characteristics of the tourism industry, 4.1.1 increase in number, 4.1.2 improvement in agglomeration degree, 4.1.3 changes in spatial structure, 4.2 factors influencing the tourism industry distribution, 4.2.1 explanatory power of influencing factors, 4.2.2 interactions of influencing factors, 5 discussion, 6 conclusions and implications, 6.1 conclusions, 6.2 implications, 6.2.1 theoretical implications, 6.2.2 practical implications.

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The temporal-spatial pattern of linear cultural heritage in the context of the tourism industry is closely linked to heritage management. Using the 1800 km long Beijing-Hangzhou Grand Canal as an example, this study compared the dynamic evolution of tourism businesses in Beijing, Liaocheng, and Yangzhou at three time points (2010, 2015, and 2019) via nearest neighbor analysis, kernel density estimation, and the standard deviational ellipse. Next, a Geo-detector was used to examine the influencing factors. The results reveal significant growth regardless of the quantity or agglomeration degree from 2010 to 2019, and the direction of industrial expansion is consistent with the flow direction of the canal. Moreover, the explanatory powers of factors related to socioeconomic development and canal resources are obviously stronger than those of the natural environment. The findings of this study offer theoretical constructs and policy recommendations for the sustainable development of the Beijing-Hangzhou Grand Canal and other linear cultural heritage sites.

Linear cultural heritage (LCH) is a new type of world heritage. It reflects inter-regional exchanges and human activities in a linear or strip geographical space during a specific period, such as military fortifications, water conservancy and transportation projects, and trade and religious routes ( Shan, 2006 ; Yu et al., 2009 ). Since the end of the 20th century, LCH has gradually become a concern for governments, academics, and the public worldwide. Unlike dot cultural heritage, such as individual cultural relic buildings, or planar cultural heritage, such as towns or village landscapes, LCH usually involves multiple administrative districts, cultural regions, and economic zones ( Zhang et al., 2020 ), so it has the characteristics of a complex structure, high interactivity, a wide spatial span, and strong cultural continuity ( Li and Zou, 2021 ).

Implemented as an effective solution for displaying local culture ( Wu and Wang, 2018 ), tourism offers feasible paths for LCH protection and activation. However, due to unbalanced resource distribution and complex spatial composition, LCH faces a significant dilemma for the different destinations along heritage sites, with the number of visitors being either too high or too low. By providing visitors with necessary services such as dining, lodging, transportation, sightseeing, and shopping ( Aratuo and Etienne, 2018 ), travel-related businesses directly present an LCH's current situation and potential as a destination. Understanding the temporal-spatial distribution of the tourism industry can clarify the development models and supporting conditions of the LCH, which is significant for different areas along the LCH according to the actual situation, and avoids inappropriate development and management.

The world's largest and longest manmade canal, the Beijing-Hangzhou Grand Canal, stretches nearly 1800 km across 22 cities that are at or above the prefecture level in eastern China. This canal is an outstanding ancient water conservancy and shipping engineering technology ( Peng, 2014 ). However, similar to other LCHs, the Beijing-Hangzhou Grand Canal is also experiencing the problem of unbalanced tourism development. Exploring the temporal-spatial distribution pattern of the tourism industry along the canal can promote the positive interaction between heritage and leisure activity, and provide theoretical guidance on heritage management and tourism marketing for LCH worldwide.

This study's aforementioned rationale is applied in the pursuit of two objectives: 1) Compare the temporal-spatial distribution of the tourism industry along the Beijing-Hangzhou Grand Canal and 2) Analyze the factors influencing the tourism industry distribution. Based on these two objectives, this study contributes to the theoretical advancement of LCH management and leisure marketing from an internal comparative perspective and can guide feasible policy formulation in a sustainable manner.

LCH represents a deep understanding of the continuous protection of cultural heritage after extending and integrating similar concepts, such as “cultural route”, “heritage corridor” and “heritage route” ( Lu, 2014 ). Compared with these concepts, LCH has a broader definition standard, which can be explained as a subcategory of cultural heritage formed by spatial morphological constraints ( Harvey, 2015 ). This study defines LCH as a cultural heritage group that relies primarily on linear spaces such as rivers, canyons, traffic lines, and commercial roads, with outstanding thematic and functional features. Studies on LCH have mainly discussed their functional evolution ( Oviedo et al., 2014 ), value assessment ( Božić and Tomić, 2016 ), spatial structure, and protection and utilization, and have mostly focused on specific administrative regions, or heritage areas with definite boundaries ( Hoşgör and Yigiter, 2011 ). However, cross-regional comparative studies within the LCH should be further explored ( Caton and Santos, 2007 ).

Tourism and leisure utilization are effective approaches for cultural heritage activation ( Wu and Wang, 2018 ). Considering the high degree of integration in the tourism and leisure industry ( Zhang et al., 2021 ), this study focuses on the extensive role of host and guest sharing; thus, it does not distinguish between the two tourism products ( Gravari-Barbas, 2018 ), brand building ( Hou and Zhang, 2019 ), or effects ( Campolo et al., 2016 ), all of which promote the diversity and richness of LCH tourism and leisure research. However, because of the outstanding universal values of LCH, most studies have overemphasized the heritage and paid insufficient attention to the external visiting environment that is related to economic and social development ( Tuxill et al., 2008 ). As a result, although the cultural connotation of LCH has been demonstrated, the driving effect of the tourism industry has not been fully explored. Tourism and leisure are derivative functions of LCH and a complex system containing many elements ( Telfer, 2001 ). Exploring the utilization pattern and evolutionary law of the tourism industry along the LCH is conducive to evaluating the development potential and promoting comprehensive benefits, especially from the perspective of the coupling of the heritage and tourism industries.

The temporal-spatial distribution illustrates the evolving process and characteristics of tourism development, which helps to clarify the layout rationale of the supply market and provides guidance for the scientific management of LCH ( Zhang et al., 2020 ). Because of the large geographical span and complex regional situation, the temporal-spatial distribution of the tourism industry along an LCH is mainly discussed in two aspects. On the one hand, the integrity of LCH determines that most studies explore its evolutionary laws from the perspective of the heritage as a whole ( Murray and Graham, 1997 ). On the other hand, some studies have focused on partial sections or regions of an LCH to support dynamic updates of localized marketing and management for the large-scale heritage ( Ren, 2017 ).

Based on empirical analyses, scholars have proposed the “node-channel-network” and “node-link-proposition-hierarchy” spatial modes, which emphasize the key position of nodes in LCH tourism ( Wang et al., 2012 ). Temporal changes in distribution can determine the reasons for the evolution of the tourism industry by distinguishing different developmental stages and facilitating the prediction of future trends ( Oviedo et al., 2014 ). Studies have generally regarded the spatial distribution of LCH tourism and leisure utilization as an evolving process. Although an increasing number of studies are available on the temporal-spatial distribution of the tourism industry of LCH, most have focused on the whole heritage or only partial sections.

Due to the various social, cultural, and political backgrounds, the geographical distribution of the LCH tourism industry tends to display diverse situations ( Ren, 2017 ). Heritage resources, tourist attractions, traffic conditions, cultural connotations, ecological environments, service facilities, tourist markets, policies, and regulations are common factors influencing the spatial layout of the LCH tourism industry ( Hoşgör and Yigiter, 2011 ; Draper et al., 2016 ; Gravari-Barbas, 2018 ; Zhou, 2021 ). The large number of factors illustrates that the tourism industry is a comprehensive system and closely bound to the heritage itself and the surrounding environment ( Zhang et al., 2020 ). A summary of the existing studies shows that three categories of factors have been mentioned frequently. First, tourism businesses usually present spatial agglomerations along the LCH, and spread out and decline to both sides ( Zhang et al., 2021 ). As the core tourist attractions, heritage resources directly affect the spatial location of tourism businesses ( Zhang et al., 2023a ). Second, LCH tourism is highly dependent on the natural environment ( Zhang et al., 2023b ). The prosperity of tourism in different sections along an LCH is significantly different under the influence of natural factors such as air quality and greening rate ( Zhang et al., 2023a ). Finally, the tourism industry is deeply rooted in the local socioeconomic environment, and economically developed sections along the LCH will stimulate tourism market vitality and build well-known tourism brands ( Zhou, 2021 ).

The temporal-spatial heterogeneity along the LCH tourism industry is the result of many factors, so revealing the influencing factors can further clarify the industrial layout principle and provide guidance on tourism marketing and destination management for practical application.

Beijing-Hangzhou Grand Canal is a vast inland waterway system, stretching from Beijing in the North China Plain to Hangzhou in the Middle and Lower Plain of Yangtze River. Constructed in sections from the 5 th century BC onward, it was regarded as the world's largest and most extensive hydraulic engineering project prior to the Industrial Revolution. Relying on diverse cultures and resources such as water conservancy, commercial trade, the royal system and local literature, there are numerous and distinctive tourism resources along the canal ( Li and Zou, 2021 ).

Most studies on the tourism industry of the Beijing-Hangzhou Grand Canal are combined with resource evaluation and development potential, involving different spatial scales such as cities, regions or the whole canal (Wang, 2018). However, like other LCHs, this nearly 1800 km canal also has the problem of unbalanced development, and the tourism industry is no exception ( Peng, 2014 ). Hence, comparing and distinguishing the different development conditions and influencing factors of the tourism industry is necessary for this canal.

Considering the heritage function and tourism development, this study selected Beijing, Liaocheng and Yangzhou for the comparative analysis ( Fig. 1 ). Specifically, although the original functions of canals, such as shipping, were barely operational in Beijing, many recreational spaces along the canal have been built to stimulate tourism activities. Canal recession also happened in Liaocheng. With the watercourse drying up or even disappearing, the heritage resources and tourism attractions are insufficient, and the tourism market development has lost vitality. Unlike the canal in the first two cities, the canal in Yangzhou has always played a significant role in shipping and water conservancy. As a canal city, Yangzhou is also one of the most prominent tourist destinations along the Beijing-Hangzhou Grand Canal. In addition, these three cities are located in the northern, middle, and southern portions of the canal, respectively, which benefits the comparison of differences along the entire canal. Therefore, this study considers different combinations of heritage and tourism to explore the issues related to the tourism industry using the most representative sections along the canal.

Although the Beijing section of the canal has not fully realized its intended function, as an urban ecological recreational space, it is receiving increasing attention. The government has strengthened relevant regulations, with participation from the community. The Beijing Section of the canal has been a model for improving water quality and preventing pollution. Since its transformation, the Canal mainly serves to improve the urban ecological environment and it plays a notable role in the urban leisure and recreation ( Table 1 ).

The Liaocheng section of the canal is in poor condition and entirely silted up, so it only offers surrounding water conservancy facilities, ancient buildings, inscriptions, and so forth. The canal flowing through the downtown area of Liaocheng became a channelized river after its renovation and is designed as a waterway for urban canal cruises ( Table 1 ). However, there are many abandoned canals in the rural areas. Although the government has conducted canal restoration, villagers remain unaware of the value of the canals. Notably, daily sewage and contamination in rural areas can lead to serious water pollution.

Study sites

The Yangzhou section is a well-protected section of the Beijing-Hangzhou Grand Canal, especially the ancient canal within the urban area. As the main landscape belt and recreational space of Yangzhou, this section contributes to urban greening, leisure activities for citizens and sightseeing for tourists ( Table 1 ). Based on the ancient canal, the main tourist business district of Yangzhou was formed by actively exploring the canal culture related to, for example, canal cruises, bank landscapes, and cultural relics.

This study mainly referred to the National Statistical Classification of Tourism and Related Industries (2018) to divide the tourism industry into five categories: tourism landscape (e.g., tourist attractions or scenic spots related to sightseeing, recreation, vacation, and folk culture), tourism shopping (e.g., shopping centers, large shopping malls, commercial blocks, and tourist souvenir shops), accommodation facilities (e.g., star-rated hotels, hostels, resorts, and homestays), leisure catering (e.g., restaurants, snack bars, bars, teahouses, and coffee shops), and entertainment (e.g., theaters, swimming pool complexes, gymnasiums, and cultural exhibition halls). Three time points (2010, 2015, and 2019) were selected for comparison to show the temporal-spatial evolution of the tourism industries in different cities. These time points were selected mainly because The Grand Canal was listed as a World Cultural Heritage in 2014. Considering that the brand effect of heritage has a huge impact on tourism, with 2015 as the first year after becoming a worldwide heritage, it basically reflects the status of applying for World Cultural Heritage. The years of 2010 and 2019 respectively reflect the development of the similar times before and after that notable change.

First, the statistics of the tourism industry in Beijing, namely, name, location, and opening time, were collected from the Beijing Statistical Yearbook, Development Plan of Tourism and Exhibition Industry during the 13th Five-Year Period of Beijing, Development Plan of Total Number and Layout of Entertainment Venues in Beijing during in 2013–2015, Statistical Communiques and Annual Work Reports of the National Economic and Social Development, and the official websites of the Beijing Municipal Bureau of Statistics (  http://tjj.beijing.gov.cn/tjsj/ ), the Beijing Municipal Bureau of Culture and Tourism (  http://whlyj.beijing.gov.cn/ ), and BIGEMAP software. Next, the databases of Liaocheng and Yangzhou were formed separately in the same manner. The tourism industry data of Liaocheng were collected from the Liaocheng Statistical Yearbook , Liaocheng Urban Master Planning ( 2014–2030 ), S tatistical Communiques and Annual Work Reports of the National Economic and Social Development , and the official websites of the Liaocheng Statistics Bureau (  http://tjj.liaocheng.gov.cn/ ), the Liaocheng Culture and Tourism Bureau (  http://wlj.liaocheng.gov.cn/ ), the Liaocheng Natural Resources and Planning Bureau (  http://zrzyhghj.liaocheng.gov.cn/ ), and BIGEMAP software. The tourism industry data of Yangzhou were collected from the Yangzhou Statistical Yearbook , Master Planning of Yangzhou Tourism Development ( 2010–2030 ), Statistical Communique on National Economic and Social Development , the official websites of the Yangzhou Statistics Bureau (  http://tjj.yangzhou.gov.cn/ ), the Cultural Radio, Television and Tourism Bureau (  http://wglj.yangzhou.gov.cn/ ), and BIGEMAP software.

Comparison of the major tourism activities along the Beijing-Hangzhou Grand Canal

The data were then verified by Baidu Maps (  https://map.baidu.com/ ) and processed using the registration and digitization functions of ArcGIS software. By performing these steps, the data for the tourism industries in Beijing, Liaocheng, and Yangzhou in 2010, 2015, and 2019 were collated ( Table 2 ).

Tourism industry data for Beijing, Liaocheng, and Yangzhou

Influencing factors and data sources

When determining the factors that affect the tourism industry along the Beijing-Hangzhou Grand Canal, this study considered the characteristics of LCH and factors that influence tourism development in general. Based on relevant studies, eight factors referring to canal resources, the natural environment and socioeconomic development were selected as the influencing factors, and the corresponding data for Beijing, Liaocheng, and Yangzhou at the three time points (2010, 2015, and 2019) were collected ( Table 3 ).

The spatial distribution pattern was defined by nearest neighbor analysis, which examines the distances between each point and the point closest to it and then compares these to the expected values in the complete random spatial pattern ( Long et al., 2018 ). Generally, the spatial distribution pattern presents one of three modes: dispersed, randomly distributed, or clustered, which can be determined by the Nearest Neighbor Index ( NNI ). This method was used in this study to examine spatial agglomeration of the tourism industry along the LCH. The calculation formula is:

where d i is the distance between each point and its nearest neighbor; n is the number of points; and A is the size of the area under study. When NNI = 1, the points are randomly distributed; when 0< NNI <1, the points are clustered; and when NNI >1, the points are dispersed.

Kernel density estimation is a non-parametric method for measuring the probability density function of variables, which provides a smooth, intuitive expression by transforming discrete points into a continuous density surface ( Yu et al., 2016 ). The kernel density map of the tourism industry was used to show the temporal-spatial changes in LCH tourism in this study. The variables of h and d were adopted as defaults. The calculation formula is:

The standard deviational ellipse (SDE) was used to represent the degree of spatial dispersion and orientation of the tourism industry. Its attribute values are the x and y coordinates for the mean center, the standard distances along the long and short axes, and the orientation of the ellipse ( Long et al., 2018 ). Specifically, the mean center denotes the central position of the arithmetic mean of tourism industry. The lengths of the long and short half axes indicate centripetal and directional feature, while the azimuth angle records the clockwise rotation angle from due north to the long axis of the ellipse. The coordinates and standard deviations of the SDE are calculated as follows:

where SDE X and SDE Y represent the coordinates of the ellipse; x i and y i are the coordinates for feature i ; x and y are the mean centers for the features; n is the total number of features; σ x and σ y are the standard deviations for the x -axis and y -axis respectively; x#x0304; i and y ̄ i are the differences between the mean center and the coordinates; and θ is the orientation of the ellipse.

Geodetector is an effective tool for exploring the causes and mechanisms that drive the spatial patterns of geographical elements. This study explored the explanatory power and interactions of different factors influencing the tourism industry distribution along the LCH according to the factor detector and interaction detector in the Geo-detector.

The factor detector in the Geo-detector is used to detect whether a certain geographical factor is the cause of the spatial distribution difference. Its theoretical core is the detection of the consistency of spatial distribution patterns between dependent and independent variables via spatial heterogeneity, to measure the explanatory degree of independent variables to the dependent variables ( Wang and Xu, 2017 ). The Geo-detector uses the power of the determinant ( q x ) to reflect the spatial correlation by using the following equation:

The interaction detector is another advantage of the Geo-detector over other statistical methods, and it verifies the interactive influences of factors ( Wang and Xu, 2017 ). The aim is to evaluate whether the combination of factors increases or decreases the explanatory power of the dependent variable.

The method of natural breaks in ArcGIS was adopted to divide each influencing factor into three grades based on the distribution law of the data. Next, this study regarded the numbers of tourism businesses within 15 km buffer zones in Beijing, Liaocheng, and Yangzhou as the dependent variables and influencing factors as the independent variables to conduct the Geo-detector analysis.

(1) Beijing section

As the capital and must-go historical destination in China, Beijing has substantial appeal to tourists, although its canal-themed tourism has not attracted much attention. To highlight the tourism potential and influence of the canal, this study used the canal as the axis to draw buffer zones within 5 km, 10 km, and 15 km, and the numbers of business points within these buffer zones were counted ( Table 4 ).

Figure 2 (a–c) shows that the buffer zone within 15 km of the canal is the core area for tourism development in Beijing, with over 65% of the businesses. Although the growth rate is lower than the rate outside the buffer zone, canal tourism has unique advantages in terms of geographical location.

(2) Liaocheng section

Liaocheng was an important shipping town in ancient times, but as the canal deteriorated, its shipping gradually declined. Considering the canal conditions and economic development of Liaocheng, buffer zones within 5 km, 10 km,and 15 km were drawn ( Fig. 2d–2f ), and the numbers of commercial businesses related to the tourism industry in the corresponding zones were counted ( Table 4 ).

Changes in the number of businesses within each buffer zone

From 2010 to 2019, tourism businesses in Liaocheng grew rapidly, spreading from a single core to a multi-core distribution mode. The improvement in tourism in the non-canal areas of Liaocheng was much higher than that along the canal; most notably, the tourism industry along the canal has not significantly changed after its designation as a World Heritage in 2014.

(3) Yangzhou section

Yangzhou is an important city and a typical representative of the Beijing-Hangzhou Grand Canal. This study extracted buffer zones within 5 km, 10 km and 15 km and the numbers of tourism businesses were counted ( Fig. 2g-2i , Table 4 ).

The distribution of tourism businesses in Yangzhou presents an obvious multi-group agglomeration pattern, with Hanjiang District as the main group, and Jiangdu District, Gaoyou City (county-level city), and Baoying County as the secondary groups. However, the tourism industry in the buffer zones improved more slowly than in other areas in the following four years, possibly because of tourism saturation and overloading of the canal areas.

The results of the NNIs revealed that businesses within 15 km of the canal were organized according to clustered patterns in 2010, 2015, and 2019 ( Table 5 ). The changes in the NNI indicate that the overall agglomeration degree of businesses weakened with the expansion of spatial distribution after 2015, although it had strengthened significantly in the previous five years. Moreover, the patterns of each type of tourism business in the different years are clustered, with lower indices than those of the overall businesses. For example, the NNIs of tourism landscape, tourism shopping, accommodation facilities, leisure catering, and entertainment in 2010 varied from 0.3 to 0.6, and all showed spatial agglomeration. The degree of agglomeration of each type improved in the following five years.

The NNIs of Liaocheng tourism businesses within the 15 km buffer zone were 0.218, 0.171, and 0.200 in 2010, 2015, and 2019, respectively ( Table 5 ). Although the degree of agglomeration increased at first and then decreased, the businesses were always clustered. Specifically, the NNIs in 2010 showed highly clustered characteristics. In 2015, the degrees of agglomeration of tourism landscape and accommodation facilities were promoted, and the other three were reduced, especially the NNI of tourism shopping which increased to 0.499. The NNIs of all the business subdivisions showed upward trends in 2019, resulting in attenuated aggregation degrees.

The NNIs of Yangzhou within the 15 km buffer zone in 2010, 2015, and 2019 were 0.134, 0.166, and 0.152, respectively ( Table 5 ). Overall, the businesses at each time point showed clustered distribution patterns, but the degree of agglomeration tended to weaken. From 2010 to 2015, the number of businesses 15 km away increased rapidly, reducing the degree of agglomeration. On this basis, the NNIs of accommodation facilities and tourism landscape continued to grow in 2019, and the tourism landscape ranked first. However, leisure catering and entertainment returned to their 2010 levels.

Distribution of businesses in Beijing, Liaocheng, and Yangzhou

The results of kernel density estimation showed that tourism businesses in Beijing from 2010 to 2019 presented a circular distribution around the high-value areas. With the continuous expansion of high-value areas, the overall distribution of businesses evolved from a small-scale mononuclear pattern to a multi-core pattern ( Fig. 3a-3c ). Equipped with perfect tourism support services, the Shichahai and Tonghui River basins in the Dongcheng and Xicheng districts were the most frequently visited destinations of the urban tourism industry. In 2019, the recreational construction along the canal in the section west of the Sihui Bridge was completed. With the development of the city subsidiary-center, Tongzhou District promoted canal culture and reshaped its landscapes by building Canal Cultural Square, Canal Olympic Park, and Tongzhou Grand Canal Forest Park; improving transportation and basic infrastructure; and creating golf clubs, resorts, and other leisure businesses.

A directional distribution analysis of the buffer zone within 5 km demonstrated that the central point of the ellipse in each of the three years remained almost unchanged, but the increase in the ellipse area indicated that the tourism industry has been expanding continually ( Table 6 ). The expansion direction of businesses was horizontal from 2010 to 2015, and both the long axis ( X -axis) and the short axis ( Y -axis) increased simultaneously over the last five years.

The distribution of tourism businesses in Liaocheng changed from single-core agglomeration to multi-core agglomeration, and then to multi-core circular agglomeration from 2010 to 2019 ( Fig. 3d-3f ). The high-density areas mainly involved Dongchangfu district and Linqing city within the 15 km buffer zone along the Beijing-Hangzhou Grand Canal. As the center of Liaocheng, Dongchangfu District relies on the Water Park, Dongchang Lake, and Nanhu Wetland Park to create an entertainment area, which conforms to Liaocheng's urban positioning of the Ancient Watery City and promotes shopping, accommodation, and other commercial activities to form the main business center. Linqing's commercial vitality is obviously weaker than that of the Dongchang District. Moreover, in Yanggu County, south of Liaocheng City, two small, high-value clusters of tourism industries have appeared successively since 2015, in the towns Qizi and Zhangqiu.

NNIs of the tourism industry types in Beijing, Liaocheng, and Yangzhou

The directional distribution of tourism businesses along the canal within the 5 km buffer zone was characterized by a continuous westward and northward movement in the past decade ( Fig. 3d-f , Table 6 ). The ellipse area expanded from 2010 to 2015, and the X -axis and Y -axis both showed substantial growth. However, the two axes shortened in the next four years, indicating the emergence of industrial concentration based on horizontal and vertical diffusion. Overall, the line of the high-value clusters located in Dongchang District and Linqing City was the developmental direction of the tourism businesses.

The high-value areas of businesses were mainly distributed in the junction of Guangling District and Hanjiang District, which were the ancient city and downtown of Yangzhou, respectively ( Fig. 3g-i ). The buffer zone within 15 km of the canal covered all high-value agglomeration areas of Yangzhou's tourism businesses, indicating that the canal was the main tourist attraction of Yangzhou. The area from south of the Slender Westlake and Benyimen Pier, west of the ancient Canal to Yinchaohe Park and Yangzhou Museum, was the main tourism industrial agglomeration area. It includes scenic spots, such as Dongguan Street, the Slender Westlake, and He Yuan, in addition to heritages listed as World Cultural Heritage sites, such as Tianning Temple, Chongning Temple, and Ge Garden. In addition, the tourism high-value clusters in Baoying County and Gaoyou City were on the right bank of the canal. The businesses are mainly distributed in the center of Baoying County, with relatively perfect marketing service facilities.

The directional distribution analysis of the buffer zone within 5 km showed that the central point of the ellipse moved to the north and east during the past decade ( Table 6 ). Specifically, it was located west of the Slender Westlake in 2010, and then moved to the west of Shaobo Lake in 2019. Simultaneously, the ellipse area continued to expand, which mainly resulted from the almost doubling of the long axis ( Fig. 3g-3i ).

The explanatory power of socioeconomic development is stronger than those of canal heritage and the natural environment ( Table 7 ). Regarding the basic information of the canal, X1 (number of heritage sites), X2 (canal water quality) and X3 (channel length) are highly associated with the distribution of tourism businesses along Beijing-Hangzhou Grand Canal, with high q values above 0.75. The q values of air quality (X4) and urban green coverage rate (X5) are the lowest among all factors, at 0.312 and 0.169, respectively, indicating that the natural environment only slightly influences the tourism industry distribution. By contrast, factors belonging to socioeconomic development possess high q values. Most notably, the value of X6 (number of tourists) reached 0.902, which ranked first among all factors. Two of the three factors in canal heritage and socioeconomic development have equal q values, while the others (X1 and X6) show different characteristics. X1 affects tourism business distribution slightly with a q value of 0.211 and X6 plays a significant role in the temporal-spatial pattern of businesses.

Table 8 shows the interaction q -statistic values of the influential factors. Generally, the explanatory power of the interaction between any two factors is higher than that of a single factor. Their interactions represent significant nonlinear enhancement, indicating that the combined effect of any two factors increases the explanatory power of the tourism industry distribution.

Directional distributions and kernel densities of businesses in Beijing, Liaocheng, and Yangzhou

Attributes of standard deviational ellipses of the tourism industries in Beijing, Liaocheng, and Yangzhou

From the explanatory power of X1 (number of heritage sites) alone, the addition of factors related to canal heritage (X2 and X3) or socioeconomic development (X6, X7, and X8) both enhance the explanatory power of tourism businesses along the Beijing-Hangzhou Grand Canal. However, the addition of air quality (X4) or urban green coverage (X5) only slightly enhanced the explanatory power, indicating that the natural environment is not very attractive to visitors and has no marketing advantage. Notably, although X4 has a low q value of 0.312, when it interacts with factors other than X1 and X5, the interactive q -statistic values exceed 0.94. A similar situation occurs with X5, which shows a significant nonlinear enhancement of the explanatory power above 0.9 when it interacts with X6 (number of tourists) or X7 (GDP).

The spatial evolution of the tourism industries in cities along the Beijing-Hangzhou Grand Canal is similar to that of cities along other LCH, and is an inevitable result of the spatial expansion along the linear space. In terms of spatial disparity, some studies have made comparisons from the perspective of the LCH as a whole ( Caton and Santos, 2007 ; Božić and Tomić, 2016 ; Zhang et al., 2020 ). However, considering the complicated microcosmic environments and rapid business expansion in the destinations ( Briedenhann and Wickens, 2004 ), it is worth comparing the tourism industry distribution in the different cities along an LCH. Businesses in Beijing, Liaocheng, and Yangzhou have presented distinctly different temporal-spatial structures, although the number and degree of agglomeration increased substantially from 2010 to 2019. Basically, the tourism industrial agglomerations along the canal are attributed to geographical proximity in these three cities, indicating that the canal remains an important impetus for regional economic and cultural development. The tendency for the direction of commercial expansion to be consistent with the flow direction of the canal appears to be the same in Beijing, Liaocheng, and Yangzhou ( Fig. 3 ). While this tendency does not mean that it is the only agglomeration mode, it still provides guides for urban tourism marketing by capturing the supply-oriented preferences. Notably, the distributions of tourism hotspots within cities require the consideration of additional extensive factors ( Deng et al., 2014 ).

Results of the factor detector

Results of the interaction detector

Although the outstanding universal value of the Beijing-Hangzhou Grand Canal is recognized globally, a substantial disparity exists in tourism development along the canal ( Li and Zou, 2021 ). Based on the temporal-spatial distribution characteristics, several key observations on the influencing factors of tourism industry distribution along the Beijing-Hangzhou Grand Canal are made. First, most studies have verified the strong correlation between heritage resources and the tourism industry along LCH (Božić and Berić,2013; Ren, 2017 ; Gravari-Barbas, 2018 ; Li, 2019 ), which further demonstrates that the quality of resources (X2 and X3) is more important than the quantity of sites (X1). In the process of transforming heritage resources into tourism products, high-quality derivative products are closely bound to a wide range of tourist markets and high satisfaction, which significantly relies on the protected status of the heritage resources themselves ( Vana and Malaescu, 2016 ). Therefore, LCH destinations should pay more attention to the marketing and publicity of high-quality resources.

Second, this study found that the natural environment plays only a small role in forming the temporal-spatial pattern of the tourism industry along the canal, which is in accordance with research conducted by Deng et al. ( 2014 ) and Zhang et al. ( 2020 ). Considering the geographical location of the Beijing-Hangzhou Grand Canal, only minor differences in the natural environment are observed among the regions ( Zhang et al., 2019 ), indicating that the ecosystem has no obvious market advantage for the cities along the canal. However, this finding is not applicable to other LCH, such as the Silk Road or the Norwegian St. Olav Pilgrim Routes.

Third, the influencing factors related to socioeconomic development are the most active, regardless of the tourism market, economic development, or transportation, all of which are crucial topics for discussion. Undoubtedly, tourism industries are deeply rooted in socioeconomic backgrounds ( Ren, 2017 ). Tourism is a complex, comprehensive industry that involves various economic and social aspects ( Briedenhann and Wickens, 2004 ). The higher the level of socioeconomic development, the more active the market atmosphere ( Du and Liu, 2011 ), which stimulates entrepreneurs' enthusiasm for tourism investment and provides adequate support from the community ( Murray and Graham, 1997 ). The temporal-spatial layout of tourism businesses is not only limited by the aforementioned factors; therefore, in-depth discussions on additional influential factors in different LCH are necessary.

Using Beijing, Liaocheng, and Yangzhou as study sites, this study explored the temporal-spatial distribution characteristics and influencing factors along the Beijing-Hangzhou Grand Canal. The results may be applicable to other LCH that are experiencing the challenge of heritage reuse and aim to develop the tourism industry. The analysis results show a continuous increase in the quantity and agglomeration degree of travel-related businesses from 2010 to 2019 in either Beijing, Liaocheng, or Yangzhou. Furthermore, the direction of industrial expansion in these three cities is consistent with the flow direction of the canal in view of the spatial structure. Moreover, the distribution characteristics of tourism businesses are found to have formed under the effects of multiple influencing factors. The explanatory powers of factors related to socioeconomic development and canal resources are stronger than those related to the natural environment.

This study analyzed the spatial evolution of the tourism industry along the Beijing-Hangzhou Grand Canal by comparing individual cities from a dynamic perspective, which enriches the theoretical research on LCH management and recreational reuse. Previous studies have assessed tourism utilization from the perspective of LCH as a whole, but few have compared the complicated microcosmic environments in areas along an LCH, especially at the city level ( Zhang et al., 2023b ). Underpinned by multidisciplinary theories and methods, this study conducted a comparative analysis of the three cities of Beijing, Liaocheng, and Yangzhou. Unlike other studies that chose one famous section with high-level tourism development, this study considered the different combinations of heritage function and tourism development to reveal the laws governing the LCH tourism industry under various special settings. Our findings on the tourism industry of the Beijing-Hangzhou Grand Canal, especially the temporal-spatial distribution laws in the three cities, enhance the research contents of tourism geography and cultural heritage management, and also improve academic research in related fields.

The identification of influencing factors is another highlight of this study. By comparing the temporal-spatial distributions of the tourism industries in three cities, this study tried to clarify the internal logic of the evolutionary mechanism and spatial differences. Although tourism development is progressing in the Beijing-Hangzhou Grand Canal, spatial disparity remains a problem that must be solved. The findings on the influencing factors provide ideas for revealing the business layouts of LCH or similar tourism resources, and are essential basic research for location theory and tourism marketing. The discussions about the explanatory powers of the different factors underscore the complex situations faced by LCH, which is conducive to dialectically treating LCH tourism and striking a balance between heritage protection and tourism development. By deepening our understanding of this heritage type, this study provides theoretical guidance for existing large-scale heritage management and policy adjustments. This also has numerous implications for the tourism marketing and sustainable optimization of the Beijing-Hangzhou Grand Canal. In addition to combining the influencing factors, further research should aim to optimize the spatial layout of travel-related businesses and formulate marketing strategies by adjusting the explanatory powers of the various factors.

Based on the above analysis of the temporal-spatial distribution of the Beijing-Hangzhou Grand Canal and tourism-related businesses, different developmental countermeasures should be adopted for the different types of cities along the canal. Taking Beijing, Liaocheng, and Yangzhou as examples, the following management responses are proposed for the improvement of tourism in the Beijing-Hangzhou Grand Canal.

For the Beijing section of the canal, it is necessary to repair or restore the canal ruins, fully excavate the canal culture, and create a unique canal image, so that the canal tourism can stand out in the fierce market competition. At the same time, efforts should be made to enhance the connections between the canal and other heritage and scenic spots, strengthen the improvements of the surrounding environment, and protect the ecological environment of the canal.

For Liaocheng section, with its damaged heritage sites and limited tourism businesses, strengthening the management of the canal and heritage is the basis and key for maintaining the canal culture. Furthermore, speeding up the environmental transformation, implementing ecological greening projects, and promoting the universal education of canal culture are all feasible solutions. In the spatial layout of the tourism industry, it is necessary to form one or several strong tourism poles to drive the rapid development of the entire canal tourism industry.

The canal tourism in Yangzhou section has a good demonstration role, benefiting from the specific regional culture, economic environment and policy measures. To achieve further optimization, the Yangzhou section should have a deep understanding of the demand of the tourist source market, formulate adaptive development plans according to the requirements of the local resource level and protection and development. At the same time, it is necessary to balance the distribution of stakeholder interests, guide the healthy competition of tourism enterprises, and avoid the loss of cultural connotation and the destruction of cultural heritage that can be caused by excessive commercialization.

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