definition of comparative case study

Comparative Case Studies: An Innovative Approach

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A comparative case study is a research method that involves an in-depth examination and comparison of two or more cases within their real-life contexts. This approach allows researchers to identify patterns, differences, and similarities across cases, which can lead to a deeper understanding of complex phenomena and help generate insights that are applicable in broader settings.

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5 Must Know Facts For Your Next Test

• Comparative case studies are often used in social sciences, business, and policy research to draw insights from diverse contexts.
• This method helps uncover causal relationships by analyzing how different factors influence outcomes across various cases.
• Comparative case studies can be qualitative or quantitative, allowing for flexibility in how data is collected and analyzed.
• The selection of cases is critical; researchers often choose cases that are either similar or varied to highlight specific aspects of interest.
• Findings from comparative case studies can contribute to theory building by providing empirical evidence that supports or challenges existing theories.

Review Questions

• A comparative case study enhances understanding by allowing researchers to analyze multiple cases simultaneously, identifying patterns and variations that may not be evident in a single case. This method highlights how different contexts influence outcomes and can reveal causal relationships between variables. By comparing cases, researchers can gain insights that are more generalized and applicable to broader situations.
• Researchers conducting comparative case studies may face challenges such as ensuring the selection of appropriate cases that provide relevant comparisons, managing the complexity of analyzing multiple datasets, and maintaining consistency in data collection methods across different contexts. Additionally, researchers must be careful about bias in interpreting findings, as different contexts may lead to varying conclusions even when similar patterns are observed.
• Using comparative case studies has a significant impact on theory development in business research by providing empirical evidence that either supports or refines existing theories. By examining various business environments and practices, researchers can identify trends and anomalies that challenge traditional views. This method encourages the development of new frameworks that account for contextual differences, leading to more robust theoretical insights applicable in diverse business scenarios.

Related terms

Case study : A detailed analysis of a specific instance or event, focusing on its context and complexities to draw meaningful conclusions.

Qualitative research : Research that emphasizes understanding human behavior and experiences through methods such as interviews, observations, and case studies.

Cross-case analysis : The process of systematically comparing multiple cases to identify common themes, patterns, or differences that can inform broader theories or practices.

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Comparative Case Study

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A comparative case study (CCS) is defined as ‘the systematic comparison of two or more data points (“cases”) obtained through use of the case study method’ (Kaarbo and Beasley 1999, p. 372). A case may be a participant, an intervention site, a programme or a policy. Case studies have a long history in the social sciences, yet for a long time, they were treated with scepticism (Harrison et al. 2017). The advent of grounded theory in the 1960s led to a revival in the use of case-based approaches. From the early 1980s, the increase in case study research in the field of political sciences led to the integration of formal, statistical and narrative methods, as well as the use of empirical case selection and causal inference (George and Bennett 2005), which contributed to its methodological advancement. Now, as Harrison and colleagues (2017) note, CCS:

“Has grown in sophistication and is viewed as a valid form of inquiry to explore a broad scope of complex issues, particularly when human behavior and social interactions are central to understanding topics of interest.”

It is claimed that CCS can be applied to detect causal attribution and contribution when the use of a comparison or control group is not feasible (or not preferred). Comparing cases enables evaluators to tackle causal inference through assessing regularity (patterns) and/or by excluding other plausible explanations. In practical terms, CCS involves proposing, analysing and synthesising patterns (similarities and differences) across cases that share common objectives.

What is involved?

Goodrick (2014) outlines the steps to be taken in undertaking CCS.

Key evaluation questions and the purpose of the evaluation: The evaluator should explicitly articulate the adequacy and purpose of using CCS (guided by the evaluation questions) and define the primary interests. Formulating key evaluation questions allows the selection of appropriate cases to be used in the analysis.

Propositions based on the Theory of Change: Theories and hypotheses that are to be explored should be derived from the Theory of Change (or, alternatively, from previous research around the initiative, existing policy or programme documentation).

Case selection: Advocates for CCS approaches claim an important distinction between case-oriented small n studies and (most typically large n) statistical/variable-focused approaches in terms of the process of selecting cases: in case-based methods, selection is iterative and cannot rely on convenience and accessibility. ‘Initial’ cases should be identified in advance, but case selection may continue as evidence is gathered. Various case-selection criteria can be identified depending on the analytic purpose (Vogt et al., 2011). These may include:

• Very similar cases
• Very different cases
• Typical or representative cases
• Extreme or unusual cases
• Deviant or unexpected cases
• Influential or emblematic cases

Identify how evidence will be collected, analysed and synthesised: CCS often applies mixed methods.

Test alternative explanations for outcomes: Following the identification of patterns and relationships, the evaluator may wish to test the established propositions in a follow-up exploratory phase. Approaches applied here may involve triangulation, selecting contradicting cases or using an analytical approach such as Qualitative Comparative Analysis (QCA). Download a Comparative Case Study here Download a longer briefing on Comparative Case Studies here

Useful resources

A webinar shared by Better Evaluation with an overview of using CCS for evaluation.

A short overview describing how to apply CCS for evaluation:

Goodrick, D. (2014). Comparative Case Studies, Methodological Briefs: Impact Evaluation 9 , UNICEF Office of Research, Florence.

An extensively used book that provides a comprehensive critical examination of case-based methods:

Byrne, D. and Ragin, C. C. (2009). The Sage handbook of case-based methods . Sage Publications.

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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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In This Article Expand or collapse the "in this article" section Comparative Education

Introduction, general overviews.

• The Early Stage
• The 19th Century
• The 20th Century to the Present
• Education and Development
• A Codified Body of Theory and Knowledge Informing the Field
• Shifts in Paradigms
• The Case Study Approach versus Large-Scale Research
• Complexity, Continua, and Transitions
• International Testing Regimes
• Higher Education Programs and Professional Societies
• Scholarly Journals and Publications
• International and Regional Education Databanks and Statistics

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Comparative Education by Robert Arnove , Stephen Franz , Patricia K. Kubow LAST REVIEWED: 29 May 2019 LAST MODIFIED: 29 May 2019 DOI: 10.1093/obo/9780199756810-0152

Comparative education is a loosely bounded field that examines the sources, workings, and outcomes of education systems, as well as leading education issues, from comprehensive, multidisciplinary, cross-national, and cross-cultural perspectives. Despite the diversity of approaches to studying relations between education and society, Arnove, et al. 1992 (cited under General Overviews ) maintains that the field is held together by a fundamental belief that education can be improved and can serve to bring about change for the better in all nations. The authors further note that comparative inquiry often has sought to discover how changes in educational provision, form, and content might contribute to the eradication of poverty or the end of gender-, class-, and ethnic-based inequities. A belief in the transformative power of education systems is aligned with three principal dimensions of the field. Arnove 2013 (cited under General Overviews ) designates these dimensions as scientific/theoretical, pragmatic/ameliorative, and global/international understanding and peace. According to Farrell 1979 (cited under General Overviews ), the scientific dimension of the field relates to theory building with comparison being absolutely essential to understanding what relationships pertain under what conditions among variables in the education system and society. Bray and Thomas 1995 (cited under General Overviews ) point out that comparison enables researchers to look at the entire world as a natural laboratory in viewing the multiple ways in which societal factors, educational policies, and practices may vary and interact in otherwise unpredictable and unimaginable ways. With regard to the pragmatic dimension, comparative educators have studied other societies to learn what works well and why. At the inception of study of comparative education as a mode of inquiry in the 19th century, pioneer Marc-Antoine Jullien de Paris (b. 1775–d. 1848) aimed at not only informing and improving educational policy, but also contributing to greater international understanding. According to Giddens 1991 , Rivzi and Lingard 2010 , and Carney 2009 (all cited under General Overviews ), international understanding has become an even more important feature of comparative education as processes of globalization increasingly require people to recognize how socioeconomic forces, emanating from what were previously considered distant and remote areas of the world, impinge upon their daily lives. The priority given to each of these dimensions varies not only across individuals but also across national and regional boundaries and epistemic communities. Yamada 2015 (cited under General Overviews ), for example, finds notable differences between the discourses and practices of North American and Japanese researchers, with the former tending to locate their research in existing theories and the latter trying to understand a particular situation before eventually finding patterns or elements applicable to a wider situation. Takayama 2011 (cited under General Overviews ) notes that one reason for differences in research traditions is the Japanese emphasis on area studies. The evolution of comparative education as a scholarly endeavor reflects changes in theories, research methodologies, and events on the world stage that have required more sophisticated responses to understanding transformations occurring within and across societies.

The references cited here include leading English-language textbooks in the field that introduce readers to the principal dimensions of comparative education, including its contributions to theory building, more informed and enlightened educational policy and practice, and international understanding and world peace. They illustrate the increasing focus of the field on how globalization impacts national education systems and, in turn, are refracted and changed by local contexts. Japan, which has one of the longest traditions of comparative studies, is included to point out differences in scholarly traditions.

Arnove, Robert F. 2013. Introduction: Reframing comparative education; The dialectic of the global and the local. In Comparative education: The dialectic of the global and the local . 4th ed. Edited by Robert F. Arnove, Carlos Alberto Torres, and Stephen Franz, 1–26. Lanham, MD: Rowman and Littlefield.

The global economy and the increasing interconnectedness of societies pose shared challenges for education worldwide. Understanding the tensions between the global and the local is necessary to reframing the field of comparative education. The global-local dialectic is explored in relation to Africa, Europe, Latin America, the Middle East, and the United States.

Arnove, Robert F., Philip G. Altbach, and Gail P. Kelly. 1992. Introduction. In Emergent issues in education . Edited by Robert F. Arnove, Philip G. Altbach, and Gail P. Kelly, 1–10. Albany: State Univ. of New York Press.

The three editors/authors discuss how the book reflects the field as it emerged in the 1990s. They review the debates over theory that have remained unresolved since they emerged in the 1960s. Issues examined include modernization without Westernization, the role of international donor agencies, the reform of educational governance, public-private relations, the changing patterns of higher education, the education of girls and women, the professionalization of teaching, and the nature of literacy campaigns.

Bray, Mark, and R. Murray Thomas. 1995. Levels of comparison in educational studies: Different insights from different literatures and the value of multilevel analysis. Harvard Educational Review 65.3: 474–491.

DOI: 10.17763/haer.65.3.g3228437224v4877

The initial conceptual framework provided by Bray and Thomas constitutes a seminal contribution to comparative education that alerts scholars to the importance of multilevel units of analysis along three dimensions: geographic/local units (ranging from world/regions/ continents to that of schools/classrooms/individuals); nonlocational demographic units (ranging from ethnic/age/religious/gender groups to entire populations); and aspects of education and society (typically subjects studied, such as curriculum, teaching methods, educational finance, and management structures).

Carney, Stephen. 2009. Negotiating policy in an age of globalization: Exploring educational “policyscapes” in Denmark, Nepal, and China. Comparative Education Review 53.1: 63–68.

DOI: 10.1086/593152

The author explores the processes of policy implementation in Denmark, Nepal, and China. Carney introduces the notion of “policyscape” (one of “hyper-neoliberalism”) as a common context for understanding change efforts at different levels of education in particular localities.

Farrell, Joseph P. 1979. The necessity of comparison in educational studies: Different insights from the salience of science and the problem of comparability. Comparative Education Review 23.1: 3–16.

DOI: 10.1086/446010

In this presidential address, Farrell affirms that all sciences are comparative. The goal of science is not only to establish that relationships exist between variables, but also to determine the range over which they exist. Farrell makes a major contribution in discussing how variables in education-society relations may not be phenomenally identical, but they can be conceptually equivalent. A body of scholarship can be gradually constructed to establish comparative education as a disciplinary field of study.

Giddens, Anthony. 1991. The consequences of modernity . Stanford, CA: Stanford Univ. Press.

Giddens discusses the nature of social institutions at the end of the 20th century. Societies are entering a stage of “high modernity”—not post-modernity—as dominant forms of social and cultural organization have not yet been radically transformed. The current stage of world development provides previously unavailable opportunities for the well-being of humanity; however, it also poses systemic dangers resulting from totalitarian governments, degrading industrial work, environmental destruction, and militarism.

Rivzi, Fazal, and Bob Lingard. 2010. Globalizing education policy . London: Routledge.

The authors critique “the rationalist approach” to policy studies that have a narrow national focus. Instead, they offer insights into how reform trends in curriculum, pedagogy, evaluation, governance, and equity policies are located within a global framework. Their conclusions call for a new imaginary of globalization that challenges the dominance of the “neoliberal construction” of the world based in economics, while strengthening social solidarity and democratic learning within and across national borders.

Takayama, Keita. 2011. Reconceptualizing the politics of Japanese education: Reimagining comparative studies of Japanese education. In Reimagining Japanese education: Borders, transfers, circulations, and the comparative . Edited by David Blake Willis and Jeremy Rappleye, 247–285. Oxford: Symposium Books.

Takayama makes a strong case for viewing a dialogic relation between Japanese and non-Japanese research traditions that enables scholars to draw upon external transformations that have occurred in Japanese society and education in what he calls the “post-post-war time.”

Yamada, Shoko. 2015. The constituent elements of comparative education in Japan: A comparison with North America. Comparative Education Review 59.2: 234–260.

DOI: 10.1086/680172

Yamada analyzes how comparative education has been discussed and practiced in Japan, based on a questionnaire completed by members of the Japan Comparative Education Society and classification of articles published in its journal between 1975 and 2011. This information is then contrasted with North American trends identified by scholars examining research by members of the Comparative and International Education Society and articles in the Comparative Education Review (cited under Scholarly Journals and Publications ).

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Lau F, Kuziemsky C, editors. Handbook of eHealth Evaluation: An Evidence-based Approach [Internet]. Victoria (BC): University of Victoria; 2017 Feb 27.

Handbook of eHealth Evaluation: An Evidence-based Approach [Internet].

Chapter 10 methods for comparative studies.

Francis Lau and Anne Holbrook .

10.1. Introduction

In eHealth evaluation, comparative studies aim to find out whether group differences in eHealth system adoption make a difference in important outcomes. These groups may differ in their composition, the type of system in use, and the setting where they work over a given time duration. The comparisons are to determine whether significant differences exist for some predefined measures between these groups, while controlling for as many of the conditions as possible such as the composition, system, setting and duration.

According to the typology by Friedman and Wyatt (2006) , comparative studies take on an objective view where events such as the use and effect of an eHealth system can be defined, measured and compared through a set of variables to prove or disprove a hypothesis. For comparative studies, the design options are experimental versus observational and prospective versus retro­­spective. The quality of eHealth comparative studies depends on such aspects of methodological design as the choice of variables, sample size, sources of bias, confounders, and adherence to quality and reporting guidelines.

In this chapter we focus on experimental studies as one type of comparative study and their methodological considerations that have been reported in the eHealth literature. Also included are three case examples to show how these studies are done.

10.2. Types of Comparative Studies

Experimental studies are one type of comparative study where a sample of participants is identified and assigned to different conditions for a given time duration, then compared for differences. An example is a hospital with two care units where one is assigned a cpoe system to process medication orders electronically while the other continues its usual practice without a cpoe . The participants in the unit assigned to the cpoe are called the intervention group and those assigned to usual practice are the control group. The comparison can be performance or outcome focused, such as the ratio of correct orders processed or the occurrence of adverse drug events in the two groups during the given time period. Experimental studies can take on a randomized or non-randomized design. These are described below.

10.2.1. Randomized Experiments

In a randomized design, the participants are randomly assigned to two or more groups using a known randomization technique such as a random number table. The design is prospective in nature since the groups are assigned concurrently, after which the intervention is applied then measured and compared. Three types of experimental designs seen in eHealth evaluation are described below ( Friedman & Wyatt, 2006 ; Zwarenstein & Treweek, 2009 ).

Randomized controlled trials ( rct s) – In rct s participants are randomly assigned to an intervention or a control group. The randomization can occur at the patient, provider or organization level, which is known as the unit of allocation. For instance, at the patient level one can randomly assign half of the patients to receive emr reminders while the other half do not. At the provider level, one can assign half of the providers to receive the reminders while the other half continues with their usual practice. At the organization level, such as a multisite hospital, one can randomly assign emr reminders to some of the sites but not others. Cluster randomized controlled trials ( crct s) – In crct s, clusters of participants are randomized rather than by individual participant since they are found in naturally occurring groups such as living in the same communities. For instance, clinics in one city may be randomized as a cluster to receive emr reminders while clinics in another city continue their usual practice. Pragmatic trials – Unlike rct s that seek to find out if an intervention such as a cpoe system works under ideal conditions, pragmatic trials are designed to find out if the intervention works under usual conditions. The goal is to make the design and findings relevant to and practical for decision-makers to apply in usual settings. As such, pragmatic trials have few criteria for selecting study participants, flexibility in implementing the intervention, usual practice as the comparator, the same compliance and follow-up intensity as usual practice, and outcomes that are relevant to decision-makers.

10.2.2. Non-randomized Experiments

Non-randomized design is used when it is neither feasible nor ethical to randomize participants into groups for comparison. It is sometimes referred to as a quasi-experimental design. The design can involve the use of prospective or retrospective data from the same or different participants as the control group. Three types of non-randomized designs are described below ( Harris et al., 2006 ).

Intervention group only with pretest and post-test design – This design involves only one group where a pretest or baseline measure is taken as the control period, the intervention is implemented, and a post-test measure is taken as the intervention period for comparison. For example, one can compare the rates of medication errors before and after the implementation of a cpoe system in a hospital. To increase study quality, one can add a second pretest period to decrease the probability that the pretest and post-test difference is due to chance, such as an unusually low medication error rate in the first pretest period. Other ways to increase study quality include adding an unrelated outcome such as patient case-mix that should not be affected, removing the intervention to see if the difference remains, and removing then re-implementing the intervention to see if the differences vary accordingly. Intervention and control groups with post-test design – This design involves two groups where the intervention is implemented in one group and compared with a second group without the intervention, based on a post-test measure from both groups. For example, one can implement a cpoe system in one care unit as the intervention group with a second unit as the control group and compare the post-test medication error rates in both units over six months. To increase study quality, one can add one or more pretest periods to both groups, or implement the intervention to the control group at a later time to measure for similar but delayed effects. Interrupted time series ( its ) design – In its design, multiple measures are taken from one group in equal time intervals, interrupted by the implementation of the intervention. The multiple pretest and post-test measures decrease the probability that the differences detected are due to chance or unrelated effects. An example is to take six consecutive monthly medication error rates as the pretest measures, implement the cpoe system, then take another six consecutive monthly medication error rates as the post-test measures for comparison in error rate differences over 12 months. To increase study quality, one may add a concurrent control group for comparison to be more convinced that the intervention produced the change.

10.3. Methodological Considerations

The quality of comparative studies is dependent on their internal and external validity. Internal validity refers to the extent to which conclusions can be drawn correctly from the study setting, participants, intervention, measures, analysis and interpretations. External validity refers to the extent to which the conclusions can be generalized to other settings. The major factors that influence validity are described below.

10.3.1. Choice of Variables

Variables are specific measurable features that can influence validity. In comparative studies, the choice of dependent and independent variables and whether they are categorical and/or continuous in values can affect the type of questions, study design and analysis to be considered. These are described below ( Friedman & Wyatt, 2006 ).

Dependent variables – This refers to outcomes of interest; they are also known as outcome variables. An example is the rate of medication errors as an outcome in determining whether cpoe can improve patient safety. Independent variables – This refers to variables that can explain the measured values of the dependent variables. For instance, the characteristics of the setting, participants and intervention can influence the effects of cpoe . Categorical variables – This refers to variables with measured values in discrete categories or levels. Examples are the type of providers (e.g., nurses, physicians and pharmacists), the presence or absence of a disease, and pain scale (e.g., 0 to 10 in increments of 1). Categorical variables are analyzed using non-parametric methods such as chi-square and odds ratio. Continuous variables – This refers to variables that can take on infinite values within an interval limited only by the desired precision. Examples are blood pressure, heart rate and body temperature. Continuous variables are analyzed using parametric methods such as t -test, analysis of variance or multiple regression.

10.3.2. Sample Size

Sample size is the number of participants to include in a study. It can refer to patients, providers or organizations depending on how the unit of allocation is defined. There are four parts to calculating sample size. They are described below ( Noordzij et al., 2010 ).

Significance level – This refers to the probability that a positive finding is due to chance alone. It is usually set at 0.05, which means having a less than 5% chance of drawing a false positive conclusion. Power – This refers to the ability to detect the true effect based on a sample from the population. It is usually set at 0.8, which means having at least an 80% chance of drawing a correct conclusion. Effect size – This refers to the minimal clinically relevant difference that can be detected between comparison groups. For continuous variables, the effect is a numerical value such as a 10-kilogram weight difference between two groups. For categorical variables, it is a percentage such as a 10% difference in medication error rates. Variability – This refers to the population variance of the outcome of interest, which is often unknown and is estimated by way of standard deviation ( sd ) from pilot or previous studies for continuous outcome.

Sample Size Equations for Comparing Two Groups with Continuous and Categorical Outcome Variables.

An example of sample size calculation for an rct to examine the effect of cds on improving systolic blood pressure of hypertensive patients is provided in the Appendix. Refer to the Biomath website from Columbia University (n.d.) for a simple Web-based sample size / power calculator.

10.3.3. Sources of Bias

There are five common sources of biases in comparative studies. They are selection, performance, detection, attrition and reporting biases ( Higgins & Green, 2011 ). These biases, and the ways to minimize them, are described below ( Vervloet et al., 2012 ).

Selection or allocation bias – This refers to differences between the composition of comparison groups in terms of the response to the intervention. An example is having sicker or older patients in the control group than those in the intervention group when evaluating the effect of emr reminders. To reduce selection bias, one can apply randomization and concealment when assigning participants to groups and ensure their compositions are comparable at baseline. Performance bias – This refers to differences between groups in the care they received, aside from the intervention being evaluated. An example is the different ways by which reminders are triggered and used within and across groups such as electronic, paper and phone reminders for patients and providers. To reduce performance bias, one may standardize the intervention and blind participants from knowing whether an intervention was received and which intervention was received. Detection or measurement bias – This refers to differences between groups in how outcomes are determined. An example is where outcome assessors pay more attention to outcomes of patients known to be in the intervention group. To reduce detection bias, one may blind assessors from participants when measuring outcomes and ensure the same timing for assessment across groups. Attrition bias – This refers to differences between groups in ways that participants are withdrawn from the study. An example is the low rate of participant response in the intervention group despite having received reminders for follow-up care. To reduce attrition bias, one needs to acknowledge the dropout rate and analyze data according to an intent-to-treat principle (i.e., include data from those who dropped out in the analysis). Reporting bias – This refers to differences between reported and unreported findings. Examples include biases in publication, time lag, citation, language and outcome reporting depending on the nature and direction of the results. To reduce reporting bias, one may make the study protocol available with all pre-specified outcomes and report all expected outcomes in published results.

10.3.4. Confounders

Confounders are factors other than the intervention of interest that can distort the effect because they are associated with both the intervention and the outcome. For instance, in a study to demonstrate whether the adoption of a medication order entry system led to lower medication costs, there can be a number of potential confounders that can affect the outcome. These may include severity of illness of the patients, provider knowledge and experience with the system, and hospital policy on prescribing medications ( Harris et al., 2006 ). Another example is the evaluation of the effect of an antibiotic reminder system on the rate of post-operative deep venous thromboses ( dvt s). The confounders can be general improvements in clinical practice during the study such as prescribing patterns and post-operative care that are not related to the reminders ( Friedman & Wyatt, 2006 ).

To control for confounding effects, one may consider the use of matching, stratification and modelling. Matching involves the selection of similar groups with respect to their composition and behaviours. Stratification involves the division of participants into subgroups by selected variables, such as comorbidity index to control for severity of illness. Modelling involves the use of statistical techniques such as multiple regression to adjust for the effects of specific variables such as age, sex and/or severity of illness ( Higgins & Green, 2011 ).

10.3.5. Guidelines on Quality and Reporting

There are guidelines on the quality and reporting of comparative studies. The grade (Grading of Recommendations Assessment, Development and Evaluation) guidelines provide explicit criteria for rating the quality of studies in randomized trials and observational studies ( Guyatt et al., 2011 ). The extended consort (Consolidated Standards of Reporting Trials) Statements for non-pharmacologic trials ( Boutron, Moher, Altman, Schulz, & Ravaud, 2008 ), pragmatic trials ( Zwarestein et al., 2008 ), and eHealth interventions ( Baker et al., 2010 ) provide reporting guidelines for randomized trials.

The grade guidelines offer a system of rating quality of evidence in systematic reviews and guidelines. In this approach, to support estimates of intervention effects rct s start as high-quality evidence and observational studies as low-quality evidence. For each outcome in a study, five factors may rate down the quality of evidence. The final quality of evidence for each outcome would fall into one of high, moderate, low, and very low quality. These factors are listed below (for more details on the rating system, refer to Guyatt et al., 2011 ).

Design limitations – For rct s they cover the lack of allocation concealment, lack of blinding, large loss to follow-up, trial stopped early or selective outcome reporting. Inconsistency of results – Variations in outcomes due to unexplained heterogeneity. An example is the unexpected variation of effects across subgroups of patients by severity of illness in the use of preventive care reminders. Indirectness of evidence – Reliance on indirect comparisons due to restrictions in study populations, intervention, comparator or outcomes. An example is the 30-day readmission rate as a surrogate outcome for quality of computer-supported emergency care in hospitals. Imprecision of results – Studies with small sample size and few events typically would have wide confidence intervals and are considered of low quality. Publication bias – The selective reporting of results at the individual study level is already covered under design limitations, but is included here for completeness as it is relevant when rating quality of evidence across studies in systematic reviews.

The original consort Statement has 22 checklist items for reporting rct s. For non-pharmacologic trials extensions have been made to 11 items. For pragmatic trials extensions have been made to eight items. These items are listed below. For further details, readers can refer to Boutron and colleagues (2008) and the consort website ( consort , n.d.).

Title and abstract – one item on the means of randomization used. Introduction – one item on background, rationale, and problem addressed by the intervention. Methods – 10 items on participants, interventions, objectives, outcomes, sample size, randomization (sequence generation, allocation concealment, implementation), blinding (masking), and statistical methods. Results – seven items on participant flow, recruitment, baseline data, numbers analyzed, outcomes and estimation, ancillary analyses, adverse events. Discussion – three items on interpretation, generalizability, overall evidence.

The consort Statement for eHealth interventions describes the relevance of the consort recommendations to the design and reporting of eHealth studies with an emphasis on Internet-based interventions for direct use by patients, such as online health information resources, decision aides and phr s. Of particular importance is the need to clearly define the intervention components, their role in the overall care process, target population, implementation process, primary and secondary outcomes, denominators for outcome analyses, and real world potential (for details refer to Baker et al., 2010 ).

10.4. Case Examples

10.4.1. pragmatic rct in vascular risk decision support.

Holbrook and colleagues (2011) conducted a pragmatic rct to examine the effects of a cds intervention on vascular care and outcomes for older adults. The study is summarized below.

Setting – Community-based primary care practices with emr s in one Canadian province. Participants – English-speaking patients 55 years of age or older with diagnosed vascular disease, no cognitive impairment and not living in a nursing home, who had a provider visit in the past 12 months. Intervention – A Web-based individualized vascular tracking and advice cds system for eight top vascular risk factors and two diabetic risk factors, for use by both providers and patients and their families. Providers and staff could update the patient’s profile at any time and the cds algorithm ran nightly to update recommendations and colour highlighting used in the tracker interface. Intervention patients had Web access to the tracker, a print version mailed to them prior to the visit, and telephone support on advice. Design – Pragmatic, one-year, two-arm, multicentre rct , with randomization upon patient consent by phone, using an allocation-concealed online program. Randomization was by patient with stratification by provider using a block size of six. Trained reviewers examined emr data and conducted patient telephone interviews to collect risk factors, vascular history, and vascular events. Providers completed questionnaires on the intervention at study end. Patients had final 12-month lab checks on urine albumin, low-density lipoprotein cholesterol, and A1c levels. Outcomes – Primary outcome was based on change in process composite score ( pcs ) computed as the sum of frequency-weighted process score for each of the eight main risk factors with a maximum score of 27. The process was considered met if a risk factor had been checked. pcs was measured at baseline and study end with the difference as the individual primary outcome scores. The main secondary outcome was a clinical composite score ( ccs ) based on the same eight risk factors compared in two ways: a comparison of the mean number of clinical variables on target and the percentage of patients with improvement between the two groups. Other secondary outcomes were actual vascular event rates, individual pcs and ccs components, ratings of usability, continuity of care, patient ability to manage vascular risk, and quality of life using the EuroQol five dimensions questionnaire ( eq-5D) . Analysis – 1,100 patients were needed to achieve 90% power in detecting a one-point pcs difference between groups with a standard deviation of five points, two-tailed t -test for mean difference at 5% significance level, and a withdrawal rate of 10%. The pcs , ccs and eq-5D scores were analyzed using a generalized estimating equation accounting for clustering within providers. Descriptive statistics and χ2 tests or exact tests were done with other outcomes. Findings – 1,102 patients and 49 providers enrolled in the study. The intervention group with 545 patients had significant pcs improvement with a difference of 4.70 ( p < .001) on a 27-point scale. The intervention group also had significantly higher odds of rating improvements in their continuity of care (4.178, p < .001) and ability to improve their vascular health (3.07, p < .001). There was no significant change in vascular events, clinical variables and quality of life. Overall the cds intervention led to reduced vascular risks but not to improved clinical outcomes in a one-year follow-up.

10.4.2. Non-randomized Experiment in Antibiotic Prescribing in Primary Care

Mainous, Lambourne, and Nietert (2013) conducted a prospective non-randomized trial to examine the impact of a cds system on antibiotic prescribing for acute respiratory infections ( ari s) in primary care. The study is summarized below.

Setting – A primary care research network in the United States whose members use a common emr and pool data quarterly for quality improvement and research studies. Participants – An intervention group with nine practices across nine states, and a control group with 61 practices. Intervention – Point-of-care cds tool as customizable progress note templates based on existing emr features. cds recommendations reflect Centre for Disease Control and Prevention ( cdc ) guidelines based on a patient’s predominant presenting symptoms and age. cds was used to assist in ari diagnosis, prompt antibiotic use, record diagnosis and treatment decisions, and access printable patient and provider education resources from the cdc . Design – The intervention group received a multi-method intervention to facilitate provider cds adoption that included quarterly audit and feedback, best practice dissemination meetings, academic detailing site visits, performance review and cds training. The control group did not receive information on the intervention, the cds or education. Baseline data collection was for three months with follow-up of 15 months after cds implementation. Outcomes – The outcomes were frequency of inappropriate prescribing during an ari episode, broad-spectrum antibiotic use and diagnostic shift. Inappropriate prescribing was computed by dividing the number of ari episodes with diagnoses in the inappropriate category that had an antibiotic prescription by the total number of ari episodes with diagnosis for which antibiotics are inappropriate. Broad-spectrum antibiotic use was computed by all ari episodes with a broad-spectrum antibiotic prescription by the total number of ari episodes with an antibiotic prescription. Antibiotic drift was computed in two ways: dividing the number of ari episodes with diagnoses where antibiotics are appropriate by the total number of ari episodes with an antibiotic prescription; and dividing the number of ari episodes where antibiotics were inappropriate by the total number of ari episodes. Process measure included frequency of cds template use and whether the outcome measures differed by cds usage. Analysis – Outcomes were measured quarterly for each practice, weighted by the number of ari episodes during the quarter to assign greater weight to practices with greater numbers of relevant episodes and to periods with greater numbers of relevant episodes. Weighted means and 95% ci s were computed separately for adult and pediatric (less than 18 years of age) patients for each time period for both groups. Baseline means in outcome measures were compared between the two groups using weighted independent-sample t -tests. Linear mixed models were used to compare changes over the 18-month period. The models included time, intervention status, and were adjusted for practice characteristics such as specialty, size, region and baseline ari s. Random practice effects were included to account for clustering of repeated measures on practices over time. P -values of less than 0.05 were considered significant. Findings – For adult patients, inappropriate prescribing in ari episodes declined more among the intervention group (-0.6%) than the control group (4.2%)( p = 0.03), and prescribing of broad-spectrum antibiotics declined by 16.6% in the intervention group versus an increase of 1.1% in the control group ( p < 0.0001). For pediatric patients, there was a similar decline of 19.7% in the intervention group versus an increase of 0.9% in the control group ( p < 0.0001). In summary, the cds had a modest effect in reducing inappropriate prescribing for adults, but had a substantial effect in reducing the prescribing of broad-spectrum antibiotics in adult and pediatric patients.

10.4.3. Interrupted Time Series on EHR Impact in Nursing Care

Dowding, Turley, and Garrido (2012) conducted a prospective its study to examine the impact of ehr implementation on nursing care processes and outcomes. The study is summarized below.

Setting – Kaiser Permanente ( kp ) as a large not-for-profit integrated healthcare organization in the United States. Participants – 29 kp hospitals in the northern and southern regions of California. Intervention – An integrated ehr system implemented at all hospitals with cpoe , nursing documentation and risk assessment tools. The nursing component for risk assessment documentation of pressure ulcers and falls was consistent across hospitals and developed by clinical nurses and informaticists by consensus. Design – its design with monthly data on pressure ulcers and quarterly data on fall rates and risk collected over seven years between 2003 and 2009. All data were collected at the unit level for each hospital. Outcomes – Process measures were the proportion of patients with a fall risk assessment done and the proportion with a hospital-acquired pressure ulcer ( hapu ) risk assessment done within 24 hours of admission. Outcome measures were fall and hapu rates as part of the unit-level nursing care process and nursing sensitive outcome data collected routinely for all California hospitals. Fall rate was defined as the number of unplanned descents to the floor per 1,000 patient days, and hapu rate was the percentage of patients with stages i-IV or unstageable ulcer on the day of data collection. Analysis – Fall and hapu risk data were synchronized using the month in which the ehr was implemented at each hospital as time zero and aggregated across hospitals for each time period. Multivariate regression analysis was used to examine the effect of time, region and ehr . Findings – The ehr was associated with significant increase in document rates for hapu risk (2.21; 95% CI 0.67 to 3.75) and non-significant increase for fall risk (0.36; -3.58 to 4.30). The ehr was associated with 13% decrease in hapu rates (-0.76; -1.37 to -0.16) but no change in fall rates (-0.091; -0.29 to 011). Hospital region was a significant predictor of variation for hapu (0.72; 0.30 to 1.14) and fall rates (0.57; 0.41 to 0.72). During the study period, hapu rates decreased significantly (-0.16; -0.20 to -0.13) but not fall rates (0.0052; -0.01 to 0.02). In summary, ehr implementation was associated with a reduction in the number of hapu s but not patient falls, and changes over time and hospital region also affected outcomes.

10.5. Summary

In this chapter we introduced randomized and non-randomized experimental designs as two types of comparative studies used in eHealth evaluation. Randomization is the highest quality design as it reduces bias, but it is not always feasible. The methodological issues addressed include choice of variables, sample size, sources of biases, confounders, and adherence to reporting guidelines. Three case examples were included to show how eHealth comparative studies are done.

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Appendix. Example of Sample Size Calculation

This is an example of sample size calculation for an rct that examines the effect of a cds system on reducing systolic blood pressure in hypertensive patients. The case is adapted from the example described in the publication by Noordzij et al. (2010) .

(a) Systolic blood pressure as a continuous outcome measured in mmHg

Based on similar studies in the literature with similar patients, the systolic blood pressure values from the comparison groups are expected to be normally distributed with a standard deviation of 20 mmHg. The evaluator wishes to detect a clinically relevant difference of 15 mmHg in systolic blood pressure as an outcome between the intervention group with cds and the control group without cds . Assuming a significance level or alpha of 0.05 for 2-tailed t -test and power of 0.80, the corresponding multipliers 1 are 1.96 and 0.842, respectively. Using the sample size equation for continuous outcome below we can calculate the sample size needed for the above study.

n = 2[(a+b)2σ2]/(μ1-μ2)2 where

n = sample size for each group

μ1 = population mean of systolic blood pressures in intervention group

μ2 = population mean of systolic blood pressures in control group

μ1- μ2 = desired difference in mean systolic blood pressures between groups

σ = population variance

a = multiplier for significance level (or alpha)

b = multiplier for power (or 1-beta)

Providing the values in the equation would give the sample size (n) of 28 samples per group as the result

n = 2[(1.96+0.842)2(202)]/152 or 28 samples per group

(b) Systolic blood pressure as a categorical outcome measured as below or above 140 mmHg (i.e., hypertension yes/no)

In this example a systolic blood pressure from a sample that is above 140 mmHg is considered an event of the patient with hypertension. Based on published literature the proportion of patients in the general population with hypertension is 30%. The evaluator wishes to detect a clinically relevant difference of 10% in systolic blood pressure as an outcome between the intervention group with cds and the control group without cds . This means the expected proportion of patients with hypertension is 20% (p1 = 0.2) in the intervention group and 30% (p2 = 0.3) in the control group. Assuming a significance level or alpha of 0.05 for 2-tailed t -test and power of 0.80 the corresponding multipliers are 1.96 and 0.842, respectively. Using the sample size equation for categorical outcome below, we can calculate the sample size needed for the above study.

n = [(a+b)2(p1q1+p2q2)]/χ2

p1 = proportion of patients with hypertension in intervention group

q1 = proportion of patients without hypertension in intervention group (or 1-p1)

p2 = proportion of patients with hypertension in control group

q2 = proportion of patients without hypertension in control group (or 1-p2)

χ = desired difference in proportion of hypertensive patients between two groups

Providing the values in the equation would give the sample size (n) of 291 samples per group as the result

n = [(1.96+0.842)2((0.2)(0.8)+(0.3)(0.7))]/(0.1)2 or 291 samples per group

From Table 3 on p. 1392 of Noordzij et al. (2010).

This publication is licensed under a Creative Commons License, Attribution-Noncommercial 4.0 International License (CC BY-NC 4.0): see https://creativecommons.org/licenses/by-nc/4.0/

• Cite this Page Lau F, Holbrook A. Chapter 10 Methods for Comparative Studies. In: Lau F, Kuziemsky C, editors. Handbook of eHealth Evaluation: An Evidence-based Approach [Internet]. Victoria (BC): University of Victoria; 2017 Feb 27.
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• Introduction
• Types of Comparative Studies
• Methodological Considerations
• Case Examples
• Example of Sample Size Calculation

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Single case studies vs. multiple case studies: A comparative study

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• Published 2017

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Introduction: Importance of Comparative Analysis

• First Online: 04 September 2024

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• Jason L. Powell 4  

Part of the book series: International Perspectives on Aging ((Int. Perspect. Aging,volume 43))

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Comparative aging research is a flourishing field, partly because funding in this area has increased in recent years. Comparing different societies and cultures seems especially fruitful for the analysis of societal and cultural factors in development over the life course. From a nomothetic perspective, the aim of comparisons is the search for similarities and commonalities in different societies and cultures; from an idiographic perspective, researchers are looking for societal and cultural specificity and distinctiveness. However, the potentials of comparative aging research are not fully realized for the time being. In many cases, there is little theorizing as to whether there should be differences (or similarities) in aging processes across countries, societies, or cultures. This chapter discusses the theoretical aims and ambitions of comparative aging research in general. Comparative theories are sketched, which could serve as a basis for comparative aging research, and aging theories are discussed, which could be modified to be used in comparative research. The rationale of comparative aging research is described and illustrated through empirical examples. Epistemological and methodological pitfalls (problems of conceptual, operational, functional, and measurement equivalence) are a substantial obstacle to comparative aging research. Hence, the merits and limitations of comparative designs and sampling procedures are considered.

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Powell, J.L. (2024). Introduction: Importance of Comparative Analysis. In: International Aging. International Perspectives on Aging, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-031-67172-2_1

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