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Independent and Dependent Variables Examples
The independent and dependent variables are key to any scientific experiment, but how do you tell them apart? Here are the definitions of independent and dependent variables, examples of each type, and tips for telling them apart and graphing them.
Independent Variable
The independent variable is the factor the researcher changes or controls in an experiment. It is called independent because it does not depend on any other variable. The independent variable may be called the “controlled variable” because it is the one that is changed or controlled. This is different from the “ control variable ,” which is variable that is held constant so it won’t influence the outcome of the experiment.
Dependent Variable
The dependent variable is the factor that changes in response to the independent variable. It is the variable that you measure in an experiment. The dependent variable may be called the “responding variable.”
Examples of Independent and Dependent Variables
Here are several examples of independent and dependent variables in experiments:
 In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score.
 You want to know which brand of fertilizer is best for your plants. The brand of fertilizer is the independent variable. The health of the plants (height, amount and size of flowers and fruit, color) is the dependent variable.
 You want to compare brands of paper towels, to see which holds the most liquid. The independent variable is the brand of paper towel. The dependent variable is the volume of liquid absorbed by the paper towel.
 You suspect the amount of television a person watches is related to their age. Age is the independent variable. How many minutes or hours of television a person watches is the dependent variable.
 You think rising sea temperatures might affect the amount of algae in the water. The water temperature is the independent variable. The mass of algae is the dependent variable.
 In an experiment to determine how far people can see into the infrared part of the spectrum, the wavelength of light is the independent variable and whether the light is observed is the dependent variable.
 If you want to know whether caffeine affects your appetite, the presence/absence or amount of caffeine is the independent variable. Appetite is the dependent variable.
 You want to know which brand of microwave popcorn pops the best. The brand of popcorn is the independent variable. The number of popped kernels is the dependent variable. Of course, you could also measure the number of unpopped kernels instead.
 You want to determine whether a chemical is essential for rat nutrition, so you design an experiment. The presence/absence of the chemical is the independent variable. The health of the rat (whether it lives and reproduces) is the dependent variable. A followup experiment might determine how much of the chemical is needed. Here, the amount of chemical is the independent variable and the rat health is the dependent variable.
How to Tell the Independent and Dependent Variable Apart
If you’re having trouble identifying the independent and dependent variable, here are a few ways to tell them apart. First, remember the dependent variable depends on the independent variable. It helps to write out the variables as an ifthen or causeandeffect sentence that shows the independent variable causes an effect on the dependent variable. If you mix up the variables, the sentence won’t make sense. Example : The amount of eat (independent variable) affects how much you weigh (dependent variable).
This makes sense, but if you write the sentence the other way, you can tell it’s incorrect: Example : How much you weigh affects how much you eat. (Well, it could make sense, but you can see it’s an entirely different experiment.) Ifthen statements also work: Example : If you change the color of light (independent variable), then it affects plant growth (dependent variable). Switching the variables makes no sense: Example : If plant growth rate changes, then it affects the color of light. Sometimes you don’t control either variable, like when you gather data to see if there is a relationship between two factors. This can make identifying the variables a bit trickier, but establishing a logical cause and effect relationship helps: Example : If you increase age (independent variable), then average salary increases (dependent variable). If you switch them, the statement doesn’t make sense: Example : If you increase salary, then age increases.
How to Graph Independent and Dependent Variables
Plot or graph independent and dependent variables using the standard method. The independent variable is the xaxis, while the dependent variable is the yaxis. Remember the acronym DRY MIX to keep the variables straight: D = Dependent variable R = Responding variable/ Y = Graph on the yaxis or vertical axis M = Manipulated variable I = Independent variable X = Graph on the xaxis or horizontal axis
 Babbie, Earl R. (2009). The Practice of Social Research (12th ed.) Wadsworth Publishing. ISBN 0495598410.
 di Francia, G. Toraldo (1981). The Investigation of the Physical World . Cambridge University Press. ISBN 9780521299251.
 Gauch, Hugh G. Jr. (2003). Scientific Method in Practice . Cambridge University Press. ISBN 9780521017084.
 Popper, Karl R. (2003). Conjectures and Refutations: The Growth of Scientific Knowledge . Routledge. ISBN 0415285941.
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Sat / act prep online guides and tips, independent and dependent variables: which is which.
General Education
Independent and dependent variables are important for both math and science. If you don't understand what these two variables are and how they differ, you'll struggle to analyze an experiment or plot equations. Fortunately, we make learning these concepts easy!
In this guide, we break down what independent and dependent variables are , give examples of the variables in actual experiments, explain how to properly graph them, provide a quiz to test your skills, and discuss the one other important variable you need to know.
What Is an Independent Variable? What Is a Dependent Variable?
A variable is something you're trying to measure. It can be practically anything, such as objects, amounts of time, feelings, events, or ideas. If you're studying how people feel about different television shows, the variables in that experiment are television shows and feelings. If you're studying how different types of fertilizer affect how tall plants grow, the variables are type of fertilizer and plant height.
There are two key variables in every experiment: the independent variable and the dependent variable.
Independent variable: What the scientist changes or what changes on its own.
Dependent variable: What is being studied/measured.
The independent variable (sometimes known as the manipulated variable) is the variable whose change isn't affected by any other variable in the experiment. Either the scientist has to change the independent variable herself or it changes on its own; nothing else in the experiment affects or changes it. Two examples of common independent variables are age and time. There's nothing you or anything else can do to speed up or slow down time or increase or decrease age. They're independent of everything else.
The dependent variable (sometimes known as the responding variable) is what is being studied and measured in the experiment. It's what changes as a result of the changes to the independent variable. An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age).
An easy way to think of independent and dependent variables is, when you're conducting an experiment, the independent variable is what you change, and the dependent variable is what changes because of that. You can also think of the independent variable as the cause and the dependent variable as the effect.
It can be a lot easier to understand the differences between these two variables with examples, so let's look at some sample experiments below.
Examples of Independent and Dependent Variables in Experiments
Below are overviews of three experiments, each with their independent and dependent variables identified.
Experiment 1: You want to figure out which brand of microwave popcorn pops the most kernels so you can get the most value for your money. You test different brands of popcorn to see which bag pops the most popcorn kernels.
 Independent Variable: Brand of popcorn bag (It's the independent variable because you are actually deciding the popcorn bag brands)
 Dependent Variable: Number of kernels popped (This is the dependent variable because it's what you measure for each popcorn brand)
Experiment 2 : You want to see which type of fertilizer helps plants grow fastest, so you add a different brand of fertilizer to each plant and see how tall they grow.
 Independent Variable: Type of fertilizer given to the plant
 Dependent Variable: Plant height
Experiment 3: You're interested in how rising sea temperatures impact algae life, so you design an experiment that measures the number of algae in a sample of water taken from a specific ocean site under varying temperatures.
 Independent Variable: Ocean temperature
 Dependent Variable: The number of algae in the sample
For each of the independent variables above, it's clear that they can't be changed by other variables in the experiment. You have to be the one to change the popcorn and fertilizer brands in Experiments 1 and 2, and the ocean temperature in Experiment 3 cannot be significantly changed by other factors. Changes to each of these independent variables cause the dependent variables to change in the experiments.
Where Do You Put Independent and Dependent Variables on Graphs?
Independent and dependent variables always go on the same places in a graph. This makes it easy for you to quickly see which variable is independent and which is dependent when looking at a graph or chart. The independent variable always goes on the xaxis, or the horizontal axis. The dependent variable goes on the yaxis, or vertical axis.
Here's an example:
As you can see, this is a graph showing how the number of hours a student studies affects the score she got on an exam. From the graph, it looks like studying up to six hours helped her raise her score, but as she studied more than that her score dropped slightly.
The amount of time studied is the independent variable, because it's what she changed, so it's on the xaxis. The score she got on the exam is the dependent variable, because it's what changed as a result of the independent variable, and it's on the yaxis. It's common to put the units in parentheses next to the axis titles, which this graph does.
There are different ways to title a graph, but a common way is "[Independent Variable] vs. [Dependent Variable]" like this graph. Using a standard title like that also makes it easy for others to see what your independent and dependent variables are.
Are There Other Important Variables to Know?
Independent and dependent variables are the two most important variables to know and understand when conducting or studying an experiment, but there is one other type of variable that you should be aware of: constant variables.
Constant variables (also known as "constants") are simple to understand: they're what stay the same during the experiment. Most experiments usually only have one independent variable and one dependent variable, but they will all have multiple constant variables.
For example, in Experiment 2 above, some of the constant variables would be the type of plant being grown, the amount of fertilizer each plant is given, the amount of water each plant is given, when each plant is given fertilizer and water, the amount of sunlight the plants receive, the size of the container each plant is grown in, and more. The scientist is changing the type of fertilizer each plant gets which in turn changes how much each plant grows, but every other part of the experiment stays the same.
In experiments, you have to test one independent variable at a time in order to accurately understand how it impacts the dependent variable. Constant variables are important because they ensure that the dependent variable is changing because, and only because, of the independent variable so you can accurately measure the relationship between the dependent and independent variables.
If you didn't have any constant variables, you wouldn't be able to tell if the independent variable was what was really affecting the dependent variable. For example, in the example above, if there were no constants and you used different amounts of water, different types of plants, different amounts of fertilizer and put the plants in windows that got different amounts of sun, you wouldn't be able to say how fertilizer type affected plant growth because there would be so many other factors potentially affecting how the plants grew.
3 Experiments to Help You Understand Independent and Dependent Variables
If you're still having a hard time understanding the relationship between independent and dependent variable, it might help to see them in action. Here are three experiments you can try at home.
Experiment 1: Plant Growth Rates
One simple way to explore independent and dependent variables is to construct a biology experiment with seeds. Try growing some sunflowers and see how different factors affect their growth. For example, say you have ten sunflower seedlings, and you decide to give each a different amount of water each day to see if that affects their growth. The independent variable here would be the amount of water you give the plants, and the dependent variable is how tall the sunflowers grow.
Experiment 2: Chemical Reactions
Explore a wide range of chemical reactions with this chemistry kit . It includes 100+ ideas for experiments—pick one that interests you and analyze what the different variables are in the experiment!
Experiment 3: Simple Machines
Build and test a range of simple and complex machines with this K'nex kit . How does increasing a vehicle's mass affect its velocity? Can you lift more with a fixed or movable pulley? Remember, the independent variable is what you control/change, and the dependent variable is what changes because of that.
Quiz: Test Your Variable Knowledge
Can you identify the independent and dependent variables for each of the four scenarios below? The answers are at the bottom of the guide for you to check your work.
Scenario 1: You buy your dog multiple brands of food to see which one is her favorite.
Scenario 2: Your friends invite you to a party, and you decide to attend, but you're worried that staying out too long will affect how well you do on your geometry test tomorrow morning.
Scenario 3: Your dentist appointment will take 30 minutes from start to finish, but that doesn't include waiting in the lounge before you're called in. The total amount of time you spend in the dentist's office is the amount of time you wait before your appointment, plus the 30 minutes of the actual appointment
Scenario 4: You regularly babysit your little cousin who always throws a tantrum when he's asked to eat his vegetables. Over the course of the week, you ask him to eat vegetables four times.
Summary: Independent vs Dependent Variable
Knowing the independent variable definition and dependent variable definition is key to understanding how experiments work. The independent variable is what you change, and the dependent variable is what changes as a result of that. You can also think of the independent variable as the cause and the dependent variable as the effect.
When graphing these variables, the independent variable should go on the xaxis (the horizontal axis), and the dependent variable goes on the yaxis (vertical axis).
Constant variables are also important to understand. They are what stay the same throughout the experiment so you can accurately measure the impact of the independent variable on the dependent variable.
What's Next?
Independent and dependent variables are commonly taught in high school science classes. Read our guide to learn which science classes high school students should be taking.
Scoring well on standardized tests is an important part of having a strong college application. Check out our guides on the best study tips for the SAT and ACT.
Interested in science? Science Olympiad is a great extracurricular to include on your college applications, and it can help you win big scholarships. Check out our complete guide to winning Science Olympiad competitions.
Quiz Answers
1: Independent: dog food brands; Dependent: how much you dog eats
2: Independent: how long you spend at the party; Dependent: your exam score
3: Independent: Amount of time you spend waiting; Dependent: Total time you're at the dentist (the 30 minutes of appointment time is the constant)
4: Independent: Number of times your cousin is asked to eat vegetables; Dependent: number of tantrums
These recommendations are based solely on our knowledge and experience. If you purchase an item through one of our links, PrepScholar may receive a commission.
Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.
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Fertilizer Experimentation, Data Analyses, and Interpretation for Developing Fertilization Recommendations—Examples with Vegetable Crop Research
Introduction.
Fertilizer recommendations contain several important factors, including fertilizer form, source, application timing, placement, and irrigation management. Another important part of a fertilizer recommendation is the amount of a particular nutrient to apply. The optimum fertilizer amount is determined from extensive field experimentation conducted for several years, at multiple locations, with several varieties, etc. Although rate is important, rate should be considered as a part of the overall fertilization management program. The important components of a fertilizer recommendation are discussed in Hochmuth and Hanlon (2010a) Principles of Sound Fertilizer Recommendations for Vegetables , available online at https://edis.ifas.ufl.edu/ss527 . This EDIS publication focuses on the research principles behind determining the optimum rate of fertilizer, including experimentation and interpreting research results for optimum crop production and quality in conjunction with minimal environmental consequences. We use examples from research with vegetable crops in Florida. How we interpret the results is as important as how we conducted the research.
The target audience for this article includes Extension state specialists, county Extension faculty members, and professionals conducting or working with research in nutrients, agrochemicals, and crop production. The authors assume that the reader has an understanding of basic probability and statistics. Statistical information presented in this publication is intended to demonstrate the process involved in fertilizer experimentation. Explanation of the statistics and their calculations is beyond the scope of this document.
Experimentation
The goal of research on fertilizer rate is to determine the amount of fertilizer needed to achieve a commercial crop yield with sufficient quality that is economically acceptable for the grower. In Florida, these types of studies take a slightly different approach depending on whether soil testing for the nutrient in question is involved. For example, rate studies with nitrogen (N) on sandy soils would not involve soil testing, but rate studies with phosphorus (P) or potassium (K) would. In the case of N on sandy soils, the researcher assumes there is minimal N supplied from the soil that would satisfy the crop nutrient requirement. In the case of P or K, a properly calibrated soil test will reveal if a response (yield and fruit quality) to the nutrient is likely or not. Rate studies are best conducted on soils low in the particular nutrient so that maximum crop response is likely and that response can be modeled.
Proper experimental design and statistical data analyses are critical to interpretation of the results. Research begins with a hypothesis or a set of hypotheses. One possible hypothesis may be that there will be no effect on yield associated with N fertilization. This hypothesis, called the null hypothesis, is evaluated with an experiment to test crop yield response against a range of N rates in a field likely to produce a large response to the addition of N fertilizer.
The researcher applies a range of fertilizer rates thought to capture the likely extent of possible crop yield responses. A zerofertilizer treatment is always included. Crop response without an actual fertilizer application demonstrates and measures the soilsupplied effects, if any. In some cases, sufficient nutrients, or at least a low portion of the crop nutrient requirement, may come from the soil, while in other cases, nutrients may come from the irrigation water.
The researcher may decide to divide the total seasonal amount of fertilizer into splitapplications, following what would likely be a recommended practice for the crop being studied. Multiple applications avoid potential large losses of fertilizer because of rainfall events, especially for nutrients that are mobile in the soil. Typically, all treatment rates are handled similarly for timing and placement of the fertilizer to minimize any confounding effects with rate.
During the growing season, the researcher may sample the plant for nutrient concentrations, using whole dried leaves and/or fresh petiole sap. These samples will help the researcher prove the response in yield was related to the plant's nutrient status. Typically, soil samples are not used because there is a chance of including a fertilizer particle in the sample, or there may be questions of where to sample if the fertilizer is applied by banding or through a drip tape. Photographs taken during the season are useful for documenting both growth and potential plant deficiency symptoms.
The crop response of interest, typically marketable yield, is measured at the appropriate harvest time(s). For vegetables, the fruits are evaluated according to USDA grade standards to detect any effects of fertilization on fruit quality (size, color, sugar content, etc.). Yields are expressed in the prevailing commercial units per area of production (e.g., 28lb boxes/acre, 42lb crates/acre, bushels/acre, tons/acre, etc.). The raw data should be plotted in a scatter diagram (Figure 1) to gain insight into the type and magnitude of response. Plotting the raw data allows the researcher to inspect for apparent atypical data points that may illustrate errors somewhere in the data entry process.
Once the data have been collected and inspected, they are analyzed statistically with analysis of variance (ANOVA). Did fertilization have a significant effect on yield? ANOVA is particularly useful in cases where a researcher might be evaluating the effect of fertilizer rate across several varieties of crop. Here, the researcher is interested in whether varieties differed in response to fertilizer, which will be exposed through a significant interaction term in the ANOVA source table. If the fertilizer treatment effect was significant, then the researcher will want to graphically present the results with a mathematical equation sometimes called a "model."
In fertilizer rate experiments, the rate of fertilizer is referred to as a continuous variable because there are many possible rates in addition to the ones the researcher selected to use in the experiment. Using ANOVA, especially if the experiment had the treatments arranged in a factorial arrangement, is a good approach to test for treatment effects and interactions. Fertilizer rate main effects can be subjected to polynomial contrasts, a statistical method to determine if there are linear or quadratic components in the overall response. Then regression methods can be applied to the continuous variable to develop an equation that explains the significant trend in response (see the section below about models).
The ANOVA statistics for a randomized completeblock N experimental design (data in Figure 1) with five replications and nine N rates indicate that one or more N rate treatments were statistically different from the others (Table 1). In this case, our null hypothesis would have been rejected. Since ANOVA tables contain estimates of several variance components, these tables should be included in research manuscripts but are seldom included. For example, other researchers may be able to use this information when summarizing numerous, similar studies. While simply reporting means and treatment effects is good for a simple research report or presentation, this method does not contain measures of variance, and the ANOVA table does.
Treatment Significance
Researchers cannot study every possible experimental treatment (rate) or combinations of treatments. In addition, there is natural variation in the field where the research will be conducted. The field may have variations in organic matter, soil pH, or moisture, all of which may lead to variations in yield response having nothing to do with the N treatment(s). Therefore, the notion of probability comes into play. What are the chances that the observed differences in yield are because of natural variation from plot to plot? This inherent variability is where statistical analysis of the data helps to sort out the differences most likely caused by treatment (N fertilization) from the socalled "noise" or random error in the production system. If we repeat the application of treatments, called replication, we can estimate the relative amount of natural variation. Experiments should always include replication as part of a properly designed experiment, one that would pass a peerreview process. Analysis of variance is the mathematical tool we use for this analysis, and with this statistical tool we can test the relative proportion of the variation due to treatment effects against the variation due to chance.
The generally accepted probability level of 0.05 (5%) is used in agricultural research as the probability that there could be a real difference when ANOVA indicates no such difference. This probability level is the level of error that scientists are willing to accept. In other words, a real difference is so rare that it is of minimal practical concern. If the experiment were repeated 20 times, there would be a 1 in 20 chance that our hypothesis would not be rejected. Said another way, if the ANOVA indicates a difference between one or more treatments, we are 95% certain that this difference is a real effect. We call these differences "significant" differences. If ANOVA detects significant differences among treatment means, then we reject our null hypothesis.
In the "real world," finding no significant differences has two major implications. First, it means that farmers should not be interested in spending extra money each year (for "insurance" applications) just to gain the rare possibility of a real crop response. These unjustified expenses would reduce profitability. The second implication is the potential negative impacts on the environment when a rate of fertilization is applied to the crop when not needed.
One common misinterpretation about treatment differences needs clarification. For example, assume an experiment was conducted to test the effect of N rate on tomato yield and the ANOVA found no significant difference between the grower rate and the recommended (lower) rate at the 5% probability level. This finding means that there is such a rare chance of a real treatment difference occurring that we can be confident the grower can reduce the commercial fertilizer rate. The actual means may be 2,950 and 2,920 boxes/acre for the grower and recommended rates, respectively. An argument could be made to someone without knowledge in statistics that the 30 boxes/acre "difference" is "worth" $600 (30 boxes at $20/box) and that amount will more than pay for the added fertilizer with the grower rate. This conclusion is erroneous because the ANOVA indicated no significant difference between the two treatment means. Therefore, the appropriate representation of the response to fertilizer is the average of the two means (i. e., 2,935 boxes per acre). Said another way, other factors on the farm impact yield more than fertilizer rate.
A more complex experiment may be to test the response of two cultivars to N rate. Here, ANOVA is used to test the significance of the main effect of N rate, the main effect of cultivar, and the interaction in the response of cultivar to N rate. There are two outcomes depending on whether or not there is an interaction of N rate and cultivar (i. e., that the cultivars differed in their response to N rate). If there was no interaction, then the response to N can be averaged using both cultivar means. If an interaction is observed, then each cultivar response must be evaluated separately.
Mathematical Descriptions of the Response (Models)
In statistical terms, fertilizer rate research employs various levels of a quantitative variable, the amount of fertilizer. If the ANOVA indicates a significant N treatment effect, as in Table 1, then the researcher will wish to further evaluate the response with the development of the mathematical model. Responses to a quantitative variable can be statistically inspected along the full range of the levels of the variable, and the responses to rates in between those actually applied in the field can be calculated. In most fertilizer experiments, a set of 4 to 5 levels of fertilizer plus a zerofertilizer control is sufficient for most models. The results can be presented graphically by an equation or model. The model can be used to predict results if a second experiment similar to the first were conducted. Models are typically developed with regression analyses.
Various models can be fit to a set of data to explain the responses. A linear model might explain a response that continues upward or downward in a straight line within the range of tested fertilizer rates. A linear response may mean the chosen range of treatments was insufficient to determine the maximum (or minimum) yield. A quadratic response is typical of crop yield in which the response increases with fertilizer rate to a point where yield approaches a maximum but then might decrease at higher rates. In other words, there is a point at which increased fertilizer does not result in a significant increase in yield. Quadratic models also typically have a linear component, meaning that as fertilizer rates increase from low to medium rates the yield also increases. At a certain point, the rate of yield increase starts to stabilize or decline.
Linear and quadratic models are the simplest equations to use for explaining crop responses to fertilizer, and they have served scientists well as long as the main interest in the research was maximizing yield. However, today there are other goals in fertilizer research, including economics and environmental issues. Several researchers have explored different models for explaining crop responses to fertilizer (see the articles in the list of references at the end of this publication). Studies have found that the quadratic model leads to overestimation of fertilizer recommendations derived from responses to fertilizer (Cerrato and Blackmer 1987; Hochmuth et al. 1993a; 1993b; 1996; Willcutts et al. 1998). If the goal of the research was to select a fertilizer rate to be used as a recommended practice, then the quadratic model will usually predict a greater fertilizer need if the maximum point from the model is taken as the putative recommendation. The maximum yield mean is not always significantly different from one or more means resulting from lesser fertilizer rates. If we inspect the plot of data in Figure 1, we might predict that there is little difference in yields among the fertilizer rates from 150 lb/acre or greater. Other models have been identified that result in a lower, but agronomically acceptable, recommended fertilizer rate, saving fertilizer expense and reducing the risk of excessive fertilizer applications that might endanger the environment.These models include the logistic and the linearplateau models. Using the data in Figure 1, these three models are illustrated in Figure 2, Figure 3, and Figure 4.
Researchers use statistics and mathematical models as tools to help explain crop response to fertilizer. We should keep in mind that models are tools, and we should exercise care in their use. The three models depicted here have been fit to the same data set first presented in Figure 1. We know from the ANOVA that crop responded to fertilizer in a significant way, but ANOVA does not identify which fertilizer rate was superior. However, each model tells a different story about the response, if we focus only on a model's parameters. The most commonly used model in agronomic and horticultural crop response research is the quadratic model (Figure 2). The quadratic model is easy to derive by computer statistical packages, and most researchers are familiar with it from their graduate training. Also, the quadratic model is easily differentiated to show a peak yield and its associated fertilizer rate.
The problem with relying solely on the quadratic model occurs on inspection of the mean yields versus fertilizer rate. It could be argued and can be shown by orthogonal contrasts that there is a levelingoff of yield. Further, this levelingoff occurs at a fertilizer rate less than the peak yield derived from the quadratic model. In an environmentally aware society, perhaps researchers should not simply interpret the quadratic model maximum as the putative fertilizer recommendation for rate.
An optional model being used by scientists more frequently is the linearplateau model (Figure 3). This model also yields critical model parameters, the plateau and the shoulder point. The plateau illustrates the notion that there is a levelingoff of crop yield response to fertilizer. However, the linearplateau model shoulder point could be argued to be too conservative as a putative fertilizer recommendation.
Several recent research studies with vegetables in Florida have illustrated the challenges with the quadratic and linearplateau models if used alone (Hochmuth et al. 1993a; 1993b). These researchers proposed using the midpoint between the shoulder point in the linearplateau model and the peak in the quadratic model as a putative recommended rate. For our data, this midpoint would be 200 lbs/acre of N fertilizer.
A third model (Figure 4), the logistic model, has been proposed by Overman and colleagues in studies with agronomic and vegetable crops (Overman et al. 1990; 1992; 1993; Willcutts et al. 1998). The logistic model is a reasonable compromise between the quadratic and linearplateau models. First, this model illustrates the law of diminishing returns. As the rate of nutrient is increased, the yield increases until an area of diminishing returns. Second, the slope of this model is not unusually steep. Third, the function does not pass through the origin; therefore, no negative yields would be predicted, nor are zero yields predicted with zero fertilizer added. Thus, this model accounts for native soil fertility. These attributes make the logistic model particularly useful for making fertilizer recommendations that avoid under or overfertilization.
In typical agronomic or horticultural crop yield response data, rarely are yields between 90% and 100% of maximum declared significantly (probability = 5%) different. Selecting 95% of maximum yield to derive the putative recommended fertilizer rate would be a conservative approach to ensure a most suitable fertilizer rate that would result in profitable yields with due diligence in considering the risk to the environment.
Using the data set above, the considerations for a fertilizer recommendation would include the following:
Quadratic model: The predicted peak crop response is 25.6 tons/acre with 270 lbs/acre N.
Linearplateau model: The plateau yield is 25 tons/acre and the shoulder point fertilizer rate is 129 lbs/acre N.
Logistic model: 95% maximum yield (25 tons/acre) occurs at 168 lbs/acre N, and 97% maximum occurs with 190 lbs/acre.
The list above shows that, depending on the level of conservatism applied, the putative fertilizer recommendation could range from 129 to 270 lbs/acre N, a 100% difference. Selecting the midpoint between the shoulder point of the linearplateau and the peak of the quadratic model or taking a conservative 97% maximum yield with the logistic model yields similar results. This analysis yields a putative fertilizer recommendation of approximately 200 lbs/acre N. Choosing 200 lbs/acre instead of 270 lbs/acre as the recommendation results in no sacrifice in yield but saves 70 lbs/acre of fertilizer. This is both an economic savings as well as a real removal of nutrient load from the environment.
An Example from Actual Research in Florida
The figures above are helpful to illustrate the principles of research and data presentation. What about actual data from Florida? There have been several research studies conducted with vegetables in Florida evaluating yield and fruit quality responses to fertilization with various models. One such study was conducted with watermelon (Figure 5).
In the watermelon study, the shoulder point for the linearplateau occurred at 26.4 kg ha 1 P or approximately 53 lbs/acre P 2 O 5 . The quadratic model maximum yield occurs with 75 kg ha  1 P or 150 lbs/acre P 2 O 5 . Statistical analysis (ANOVA and contrasts) of the data showed no significant difference in yield from 50 to 200 lbs/acre P 2 O 5 . The shoulder value is on the verge of steep yield reduction with less than 53 lbs/acre P 2 O 5 , but the quadratic maximum yield occurred with excessive fertilization. The authors of this research paper proposed using the midpoint between the linearplateau shoulder point and the quadratic maximum point as a reasonable compromise fertilization recommendation. In this case, the recommendation could be about 100 lbs/acre P 2 O 5 . This recommendation would result in considerable savings in P fertilizer compared to the current recommendation of 160 lbs/acre P 2 O 5 for soils with low or very low Mehlich1 P concentration.
Using the logistic model (Figure 6) yields a conclusion similar to using the midpoint between the quadratic maximum and the shoulder point of the linearplateau model. Using 97% of the maximum yield would result in a fertilizer recommendation of approximately 55 kg/ha P or 115 lbs/acre P 2 O 5 .
There are additional reasons (beyond environmental) for making recommendations closer to the conservative side of the response curve. There are numerous research reports about excessive fertilization, especially N, having a negative impact on yield and fruit quality. The slight depression in yield at excessive fertilizer rates, coupled with the cost of the extra fertilizer, may lead to significant reductions in farm profits. Furthermore, research results have been published in the peerreviewed literature documenting reductions in fruit and vegetable quality parameters by excessive fertilization (Hochmuth et al. 1996; 1999).
Some Comments about Percent Relative Yield (RY)
Crop responses are an integration of many different aspects of the entire production system to which the crop is exposed. Research completed during one season is affected by the crop integration process during that entire season, as well as some antecedent contributors, such as nitrogen mineralization from crop residue or soil organic matter. The problem with crop responses associated with different experiments conducted by separate research groups, and often for different purposes, is that the observed crop yields in each of the individual experiments will display variation. Plotting all the data from many experiments in the original units yields a scattergraph that renders a general interpretation very difficult. One method that can be used to get a sense of the crop response to fertilization across numerous studies is the percent relative yield . The highest yield obtained in that particular experiment in that particular season is assigned as 100% relative yield. All other yields are calculated by dividing the observed yield by the highest actual yield and are expressed as a percentage.
Transforming the original data in this manner adds to the flexibility of looking at the relative yields, which have been brought to a common scale. The value of this type of transformation is that researchers get a sense of how that particular crop responded to fertilizer additions throughout many seasons, locations, and production practices. Relative yield should be used with caution to avoid putting too much emphasis on this data transformation and resulting graph alone. For example, using all the RY values from several experiments for subsequent regression can be quite misleading, especially for calculating actual yields. However, noticing that the variability among all responses decreases after fertilizer rate exceeds a certain range becomes quite obvious.
There are a number of assumptions built into this transformation process. The primary assumption is that most or all of the response that we note in an RY graph is due to fertilizer. There have been extensive arguments both for and against making this assumption. In summarizing this debate, Black (1992) indicates that the assumption can be considered valid when using the RY plot to explore variation across the years, seasons, and other production practices. Black cautions the reader to avoid additional statistical evaluations of the RY plot due in part to its statistical characteristics (not normally distributed) and the true shape of the yield response to added fertilizer is sitespecific. The RY plot generalizes the sitespecific variations in nature of soil, fertilizer, climate, and plant interactions. Problems with this generalization are avoided if the RY plot is not used for subsequent regression analysis involving actual yields and further interpretation.
For those who are interested in statistics, this type of transformation also has a weighting factor based upon the selection of the maximum yield. Again, this weighting factor makes the assumptions above and is reduced to insignificance by using the RY plot on a visual basis only and not trying to further statistically analyze the regression by other means. Black (1992) states that while these objections are worthy of note, the RY plot can be a useful tool in fertilizer research.
To further illustrate the usefulness of the percent relative yield approach, watermelon yield is plotted in Figure 7. Note that the yields increase in all experiments and then tend to level off somewhere between 100 and 200 lbs/acre N. The current UF/IFAS N recommendation is 150 lbs/acre N. While this graph was not used to set the UF/IFAS recommendation, the graph indicates that the recommendation is reasonable and supported by research.
Crop fertilizer response research should be carefully conducted to account for the economics to the grower and protection of the environment from nutrient losses due to excessive fertilization. There are several mathematical models to describe crop yield response to fertilizer, and these models should be employed with caution. Using a single model to explain crop response may not account for economics and potential environmental impact together. This problem is evident with the quadratic and linearplateau models. Incorporating both models in the data response interpretation and calculating the midpoint as we have demonstrated above will consider both goals. The logistic model appears to be the best single model at considering both economics and environmental goals. There is increasing accumulation of research documenting the impacts of overfertilization on yield and quality, thus reducing profits. Added to these reasons is the need to protect the environment from nutrient pollution related to farming activities. It becomes evident that how research is conducted and how the data are analyzed and interpreted are critical to developing an informed fertilizer recommendation.
Black, C. A. 1992. Soil Fertility Evaluation and Control . Boca Raton, FL: Lewis Publishers.
Bullock, D. G., and D. S. Bullock. 1994. "Quadratic and Quadraticplusplateau Models for Predicting Optimal Nitrogen Rate of Corn: A Comparison." Agron. J. 86:1915.
Cerrato, M. E., and A. M. Blackmer. 1987. "Comparison of Models for Describing Corn Yield Response to Nitrogen Fertilizer." Agron. J. 82:13843.
Dahnke, W. C., and R. A. Olson. 1990. "Soil Test Correlation, Calibration, and Recommendation." In Soil Testing and Plant Analysis , 3 rd edition, edited by R. L. Westerman, 4571. Madison, WI: Soil Sci. Soc. Amer.
Hochmuth, G. J., E. E. Albregts, C. C. Chandler, J. Cornell, and J. Harrison. 1996. "Nitrogen Fertigation Requirements of Dripirrigated Strawberries." J. Amer. Soc. Hort. Sci. 121:6605.
Hochmuth, G. J., J. K. Brecht, and M. J. Bassett. 1999. "N Fertilization to Maximize Carrot Yield and Quality on a Sandy Soil." HortScience 34(4): 6415.
Hochmuth, G. J., J. Brecht, and M. J. Bassett. 2006. "FreshMarket Carrot Yield and Quality Responses to K Fertilization of a Sandy Soil Validated by Mehlich1 Soil Test." HortTechnology 16:2706.
Hochmuth, G. J., and E. A. Hanlon. 2010a. Principles of Sound Fertilizer Recommendations . SL315. Gainesville: University of Florida Institute of Food and Agricultural Sciences. https://edis.ifas.ufl.edu/ss527 .
Hochmuth, G. J., and E. A. Hanlon. 2010b. Summary of N, P, and K Research with Watermelon in Florida. SL325. Gainesville: University of Florida Institute of Food and Agricultural Sciences. https://edis.ifas.ufl.edu/cv232 .
Hochmuth, G. J., E. A. Hanlon, and J. Cornell. 1993a. "Watermelon Phosphorus Requirements in Soils with Low Mehlich1 Extractable Phosphorus." HortScience 28:6302.
Hochmuth, G. J., R. C. Hochmuth, M. E. Donley, and E. A. Hanlon. 1993b. "Eggplant Yield in Response to Potassium Fertilization on Sandy Soil." HortScience 28:10025.
Nelson, L. A., and R. L. Anderson. 1977. "Partitioning of Soiltest Response Probability." In Soil Testing: Correlation and Interpreting the Analytical Results, spec. publ. 29, edited by T.R. Peck, J.T. Cope, and D.A. Whitney, 1938. Madison, WI: Am. Soc. Agron.
Overman, A. R., F. G. Martin, and S. R. Wilkinson. 1990. "A Logistic Equation for Yield Response of Forage Grass to Nitrogen." Commun. Soil. Sci. Plant Anal. 21:595609.
Overman, A. R., M. A. Sanderson, and R. M. Jones. 1993. "Logistic Response of Bermudagrass and Bunchgrass Cultivars to Applied Nitrogen." Agron. J. 85:5415.
Overman, A. R., and S. R. Wilkinson. 1992. "Model Evaluation for Perennial Grasses in the Southern United States." Agron. J. 84:5239.
Willcutts, J. F., A. R. Overman, G. J. Hochmuth, D. J. Cantliffe, and P. Soundy. 1998. "A Comparison of Three Mathematical Models of Response to Applied Nitrogen: A Case Study Using Lettuce." HortScience 33:8336.
Analysis of variance for the data in Figure 1, testing crop response to rate of N fertilizer. In this case, the experimental design was a randomized, completeblock design with 5 replications.





N rate  8  1655.4  206.9  163 (P<.0001) 
Replication  4  1.5  0.4  0.3 (P=0.87) 
Error  32  40.4  1.3  
Total  44  1697.4 
Publication # SL345
Release Date: January 31, 2018
Reviewed At: January 14, 2022
Related Experts
Hochmuth, george j..
Specialist/SSA/RSA
University of Florida
Hanlon, Edward A.
Related units.
Soil and Water Science
Related topics, crop modeling, fertilization and plant nutrition.
 DOI: 10.32473/edisss5482011
 Critical Issue: Other
About this Publication
This document is SL345, one of a series of the Department of Soil and Water Sciences, UF/IFAS Extension. Original publication date March 2011. Visit the EDIS website at https://edis.ifas.ufl.edu for the currently supported version of this publication.
About the Authors
George Hochmuth, professor, Department of Soil and Water Sciences; Ed Hanlon, professor, UF/IFAS Southwest Florida Research and Education Center, Department of Soil and Water Sciences; and Allen Overman, professor, Agricultural and Biological Engineering Department; UF/IFAS Extension, Gainesville, FL 32611.
 George Hochmuth
 Rao Mylavarapu
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1.2: Science Experiments
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So what exactly is an experiment?
At first you may picture a science laboratory with microscopes and chemicals and people in white lab coats. But do all experiments have to be done in a lab? And do all scientists have to wear lab coats?
Experiments
Figure below shows a laboratory experiment involving plants. An experiment is a special type of scientific investigation that is performed under controlled conditions, usually in a laboratory. Some experiments can be very simple, but even the simplest can contribute important evidence that helps scientists better understand the natural world. An example experiment can be seen here http://www.youtube.com/watch?v=dVRBDRAsP6U or here http ://www.youtube.com/watch?v=F10EyGwd57M . As many different types of of experiments are possible, an experiment must be designed to produce data that can help confirm or reject the hypothesis .
A laboratory experiment studying plant growth. What might this experiment involve?
In this experiment, a scientist is conducting research (and taking notes) while looking through a microscope.
Medicine From the Ocean Floor
Scientists at the University of California, Santa Cruz are looking to perhaps the largest resource yet to be explored for its medical potential: the ocean. And they are taping this resource with some stateoftheart technology. These scientists are using robots to sort through thousands of marine chemicals in search of cures for diseases like cholera, breast cancer , and malaria. These experiments are described in the following KQED links:
 www.kqed.org/quest/blog/2009/...eoceanfloor/
 www.kqed.org/quest/radio/medicinefromtheoceanfloor
 science.kqed.org/quest/slides...oorslideshow/
An experiment generally tests how one variable is affected by another. The affected variable is called the dependent variable . In the plant experiment shown above, the dependent variable is plant growth. The variable that affects the dependent variable is called the independent variable . In the plant experiment, the independent variable could be fertilizer—some plants will get fertilizer, others will not. The scientists change the amount of the independent variable (the fertilizer) to observe the effects on the dependent variable (plant growth). An experiment needs to be run simultaneously in which no fertilizer is given to the plant. This would be known as a control experiment. In any experiment, other factors that might affect the dependent variable must be controlled. In the plant experiment, what factors do you think should be controlled? ( Hint: What other factors might affect plant growth?)
Sample Size and Repetition
The sample in an experiment or other investigation consists of the individuals or events that are studied, and the size of the sample (or sample size ) directly affects the interpretation of the results. Typically, the sample is much smaller than all such individuals or events that exist in the world. Whether the results based on the sample are true in general cannot be known for certain. However, the larger the sample is, the more likely it is that the results are generally true.
Similarly, the more times that an experiment is repeated (which is known as repetition ) and the same results obtained, the more likely the results are valid. This is why scientific experiments should always be repeated.
BioInspiration: Nature as Muse
For hundreds of years, scientists have been using design ideas from structures in nature. Now, biologists and engineers at the University of California, Berkeley are working together to design a broad range of new products, such as lifesaving millirobots modeled on the way cockroaches run and adhesives based on the amazing design of a gecko's foot. This process starts with making observations of nature, which lead to asking questions and to the additional aspects of the scientific process . BioInspiration: Nature as Muse can be observed at www.kqed.org/quest/television...natureasmuse.
Super Microscopes
Microscopes are arguably one of the most important tools of the biologist. They allow the visualization of smaller and smaller biological organisms and molecules. With greatly magnified powers, these instruments are becoming increasingly important in modern day research. See the following KQED videos for additional information on these remarkable tools.
 Super Microscope at http://science.kqed.org/quest/video/supermicroscope/ .
 The World's Most Powerful Microscope at http://www.youtube.com/watch?v=sCYX_XQgnSA .
 An experiment is a special type of scientific investigation that is performed under controlled conditions, usually in a laboratory.
 An experiment generally tests how one variable is affected by another.
 The sample size in an experiment directly affects the interpretation of the results.
 Repetition is the repeating of an experiment, validating the results.
Explore More
Use this resource to answer the questions that follow.
 What is an Experiment? at http://chemistry.about.com/od/introductiontochemistry/a/WhatIsAnExperiment.htm .
 Describe controlled experiments.
 Describe field experiments.
 What is a variable? Give an example.
 What are the independent and dependent variables?
 Why is it best to only have one independent variable in an experiment?
 What is an experiment?
 Compare the dependent variable to the independent variable.
 Identify the independent and dependent variables in the following experiment: A scientist grew bacteria on gel in her lab. She wanted to find out if the bacteria would grow faster on gel A or gel B. She placed a few bacteria on gel A and a few on gel B. After 24 hours, she observed how many bacteria were present on each type of gel.
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Statistics By Jim
Making statistics intuitive
Independent and Dependent Variables: Differences & Examples
By Jim Frost 15 Comments
In this post, learn the definitions of independent and dependent variables, how to identify each type, how they differ between different types of studies, and see examples of them in use.
What is an Independent Variable?
Independent variables (IVs) are the ones that you include in the model to explain or predict changes in the dependent variable. The name helps you understand their role in statistical analysis. These variables are independent . In this context, independent indicates that they stand alone and other variables in the model do not influence them. The researchers are not seeking to understand what causes the independent variables to change.
Independent variables are also known as predictors, factors , treatment variables, explanatory variables, input variables, xvariables, and righthand variables—because they appear on the right side of the equals sign in a regression equation. In notation, statisticians commonly denote them using Xs. On graphs, analysts place independent variables on the horizontal, or X, axis.
In machine learning, independent variables are known as features.
For example, in a plant growth study, the independent variables might be soil moisture (continuous) and type of fertilizer (categorical).
Statistical models will estimate effect sizes for the independent variables.
Relate post : Effect Sizes in Statistics
Including independent variables in studies
The nature of independent variables changes based on the type of experiment or study:
Controlled experiments : Researchers systematically control and set the values of the independent variables. In randomized experiments, relationships between independent and dependent variables tend to be causal. The independent variables cause changes in the dependent variable.
Observational studies : Researchers do not set the values of the explanatory variables but instead observe them in their natural environment. When the independent and dependent variables are correlated, those relationships might not be causal.
When you include one independent variable in a regression model, you are performing simple regression. For more than one independent variable, it is multiple regression. Despite the different names, it’s really the same analysis with the same interpretations and assumptions.
Determining which IVs to include in a statistical model is known as model specification. That process involves indepth research and many subjectarea, theoretical, and statistical considerations. At its most basic level, you’ll want to include the predictors you are specifically assessing in your study and confounding variables that will bias your results if you don’t add them—particularly for observational studies.
For more information about choosing independent variables, read my post about Specifying the Correct Regression Model .
Related posts : Randomized Experiments , Observational Studies , Covariates , and Confounding Variables
What is a Dependent Variable?
The dependent variable (DV) is what you want to use the model to explain or predict. The values of this variable depend on other variables. It is the outcome that you’re studying. It’s also known as the response variable, outcome variable, and lefthand variable. Statisticians commonly denote them using a Y. Traditionally, graphs place dependent variables on the vertical, or Y, axis.
For example, in the plant growth study example, a measure of plant growth is the dependent variable. That is the outcome of the experiment, and we want to determine what affects it.
How to Identify Independent and Dependent Variables
If you’re reading a study’s writeup, how do you distinguish independent variables from dependent variables? Here are some tips!
Identifying IVs
How statisticians discuss independent variables changes depending on the field of study and type of experiment.
In randomized experiments, look for the following descriptions to identify the independent variables:
 Independent variables cause changes in another variable.
 The researchers control the values of the independent variables. They are controlled or manipulated variables.
 Experiments often refer to them as factors or experimental factors. In areas such as medicine, they might be risk factors.
 Treatment and control groups are always independent variables. In this case, the independent variable is a categorical grouping variable that defines the experimental groups to which participants belong. Each group is a level of that variable.
In observational studies, independent variables are a bit different. While the researchers likely want to establish causation, that’s harder to do with this type of study, so they often won’t use the word “cause.” They also don’t set the values of the predictors. Some independent variables are the experiment’s focus, while others help keep the experimental results valid.
Here’s how to recognize independent variables in observational studies:
 IVs explain the variability, predict, or correlate with changes in the dependent variable.
 Researchers in observational studies must include confounding variables (i.e., confounders) to keep the statistical results valid even if they are not the primary interest of the study. For example, these might include the participants’ socioeconomic status or other background information that the researchers aren’t focused on but can explain some of the dependent variable’s variability.
 The results are adjusted or controlled for by a variable.
Regardless of the study type, if you see an estimated effect size, it is an independent variable.
Identifying DVs
Dependent variables are the outcome. The IVs explain the variability or causes changes in the DV. Focus on the “depends” aspect. The value of the dependent variable depends on the IVs. If Y depends on X, then Y is the dependent variable. This aspect applies to both randomized experiments and observational studies.
In an observational study about the effects of smoking, the researchers observe the subjects’ smoking status (smoker/nonsmoker) and their lung cancer rates. It’s an observational study because they cannot randomly assign subjects to either the smoking or nonsmoking group. In this study, the researchers want to know whether lung cancer rates depend on smoking status. Therefore, the lung cancer rate is the dependent variable.
In a randomized COVID19 vaccine experiment , the researchers randomly assign subjects to the treatment or control group. They want to determine whether COVID19 infection rates depend on vaccination status. Hence, the infection rate is the DV.
Note that a variable can be an independent variable in one study but a dependent variable in another. It depends on the context.
For example, one study might assess how the amount of exercise (IV) affects health (DV). However, another study might study the factors (IVs) that influence how much someone exercises (DV). The amount of exercise is an independent variable in one study but a dependent variable in the other!
How Analyses Use IVs and DVs
Regression analysis and ANOVA mathematically describe the relationships between each independent variable and the dependent variable. Typically, you want to determine how changes in one or more predictors associate with changes in the dependent variable. These analyses estimate an effect size for each independent variable.
Suppose researchers study the relationship between wattage, several types of filaments, and the output from a light bulb. In this study, light output is the dependent variable because it depends on the other two variables. Wattage (continuous) and filament type (categorical) are the independent variables.
After performing the regression analysis, the researchers will understand the nature of the relationship between these variables. How much does the light output increase on average for each additional watt? Does the mean light output differ by filament types? They will also learn whether these effects are statistically significant.
Related post : When to Use Regression Analysis
Graphing Independent and Dependent Variables
As I mentioned earlier, graphs traditionally display the independent variables on the horizontal Xaxis and the dependent variable on the vertical Yaxis. The type of graph depends on the nature of the variables. Here are a couple of examples.
Suppose you experiment to determine whether various teaching methods affect learning outcomes. Teaching method is a categorical predictor that defines the experimental groups. To display this type of data, you can use a boxplot, as shown below.
The groups are along the horizontal axis, while the dependent variable, learning outcomes, is on the vertical. From the graph, method 4 has the best results. A oneway ANOVA will tell you whether these results are statistically significant. Learn more about interpreting boxplots .
Now, imagine that you are studying people’s height and weight. Specifically, do height increases cause weight to increase? Consequently, height is the independent variable on the horizontal axis, and weight is the dependent variable on the vertical axis. You can use a scatterplot to display this type of data.
It appears that as height increases, weight tends to increase. Regression analysis will tell you if these results are statistically significant. Learn more about interpreting scatterplots .
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Reader Interactions
April 2, 2024 at 2:05 am
Hi again Jim
Thanks so much for taking an interest in New Zealand’s Equity Index.
Rather than me trying to explain what our Ministry of Education has done, here is a link to a fairly short paper. Scroll down to page 4 of this (if you have the inclination) – https://fyi.org.nz/request/21253/response/80708/attach/4/1301098%20Response%20and%20Appendix.pdf
The Equity Index is used to allocate only 4% of total school funding. The most advantaged 5% of schools get no “equity funding” and the other 95% get a share of the equity funding pool based on their index score. We are talking a maximum of around $1,000NZD per child per year for the most disadvantaged schools. The average amount is around $200$300 per child per year.
My concern is that I thought the dependent variable is the thing you want to explain or predict using one or more independent variables. Choosing the form of dependent variable that gets a good fit seems to be answering the question “what can we predict well?” rather than “how do we best predict the factor of interest?” The factor is educational achievement and I think this should have been decided upon using theory rather than experimentation with the data.
As it turns out, the Ministry has chosen a measure of educational achievement that puts a heavy weight on achieving an “excellence” rating on a qualification and a much lower weight on simply gaining a qualification. My reading is that they have taken what our universities do when looking at which students to admit.
It doesn’t seem likely to me that a heavy weighting on excellent achievement is appropriate for targeting extra funding to schools with a lot of underachieving students.
However, my stats knowledge isn’t extensive and it’s definitely rusty, so your thoughts are most helpful.
Regards Kathy Spencer
April 1, 2024 at 4:08 pm
Hi Jim, Great website, thank you.
I have been looking at New Zealand’s Equity Index which is used to allocate a small amount of extra funding to schools attended by children from disadvantaged backgrounds. The Index uses 37 socioeconomic measures relating to a child’s and their parents’ backgrounds that are found to be associated with educational achievement.
I was a bit surprised to read how they had decided on the dependent variable to be used as the measure of educational achievement, or dependent variable. Part of the process was as follows “Each measure was tested to see the degree to which it could be predicted by the socioeconomic factors selected for the Equity Index.”
Any comment?
Many thanks Kathy Spencer
April 1, 2024 at 9:20 pm
That’s a very complex study and I don’t know much about it. So, that limits what I can say about it. But I’ll give you a few thoughts that come to mind.
This method is common in educational and social research, particularly when the goal is to understand or mitigate the impact of socioeconomic disparities on educational outcomes.
There are the usual concerns about not confusing correlation with causation. However, because this program seems to quantify barriers and then provide extra funding based on the index, I don’t think that’s a problem. They’re not attempting to adjust the socioeconomic measures so no worries about whether they’re directly causal or not.
I might have a small concern about cherry picking the model that happens to maximize the Rsquared. Chasing the Rsquared rather than having theory drive model selecting is often problematic. Chasing the best fit increases the likelihood that the model fits this specific dataset best by random chance rather than being truly the best. If so, it won’t perform as well outside the dataset used to fit the model. Hopefully, they validated the predicted ability of the model using other data.
However, I’m not sure if the extra funding is determined by the model? I don’t know if the index value is calculated separately outside the candidate models and then fed into the various models. Or does the choice of model affect how the index value is calculated? If it’s the former, then the funding doesn’t depend on a potentially cherry picked model. If the latter, it does.
So, I’m not really clear on the purpose of the model. I’m guessing they just want to validate their Equity Index. And maximizing the Rsquared doesn’t really say it’s the best Index but it does at least show that it likely has some merit. I’d be curious how the took the 37 measures and combined them to one index. So, I have more questions than answers. I don’t mean that in a critical sense. Just that I know almost nothing about this program.
I’m curious, what was the outcome they picked? How high was the Rsquared? And what were your concerns?
February 6, 2024 at 6:57 pm
Excellent explanation, thank you.
February 5, 2024 at 5:04 pm
Thank you for this insightful blog. Is it valid to use a dependent variable delivered from the mean of independent variables in multiple regression if you want to evaluate the influence of each unique independent variable on the dependent variables?
February 5, 2024 at 11:11 pm
It’s difficult to answer your question because I’m not sure what you mean that the DV is “delivered from the mean of IVs.” If you mean that multiple IVs explain changes in the DV’s mean, yes, that’s the standard use for multiple regression.
If you mean something else, please explain in further detail. Thanks!
February 6, 2024 at 6:32 am
What I meant is; the DV values used as parameters for multiple regression is basically calculated as the average of the IVs. For instance:
From 3 IVs (X1, X2, X3), Y is delivered as :
Y = (Sum of all IVs) / (3)
Then the resulting Y is used as the DV along with the initial IVs to compute the multiple regression.
February 6, 2024 at 2:17 pm
There are a couple of reasons why you shouldn’t do that.
For starters, Yhat (the predicted value of the regression equation) is the mean of the DV given specific values of the IV. However, that mean is calculated by using the regression coefficients and constant in the regression equation. You don’t calculate the DV mean as the sum of the IVs divided by the number of IVs. Perhaps given a very specific subjectarea context, using this approach might seem to make sense but there are other problems.
A critical problem is that the Y is now calculated using the IVs. Instead, the DVs should be measured outcomes and not calculated from IVs. This violates regression assumptions and produces questionable results.
Additionally, it complicates the interpretation. Because the DV is calculated from the IV, you know the regression analysis will find a relationship between them. But you have no idea if that relationship exists in the real world. This complication occurs because your results are based on forcing the DV to equal a function of the IVs and do not reflect realworld outcomes.
In short, DVs should be realworld outcomes that you measure! And be sure to keep your IVs and DV independent. Let the regression analysis estimate the regression equation from your data that contains measured DVs. Don’t use a function to force the DV to equal some function of the IVs because that’s the opposite direction of how regression works!
I hope that helps!
September 6, 2022 at 7:43 pm
Thank you for sharing.
March 3, 2022 at 1:59 am
Excellent explanation.
February 13, 2022 at 12:31 pm
Thanks a lot for creating this excellent blog. This is my goto resource for Statistics.
I had been pondering over a question for sometime, it would be great if you could shed some light on this.
In linear and nonlinear regression, should the distribution of independent and dependent variables be unskewed? When is there a need to transform the data (say, BoxCox transformation), and do we transform the independent variables as well?
October 28, 2021 at 12:55 pm
If I use a independent variable (X) and it displays a low pvalue <.05, why is it if I introduce another independent variable to regression the coefficient and pvalue of Y that I used in first regression changes to look insignificant? The second variable that I introduced has a low pvalue in regression.
October 29, 2021 at 11:22 pm
Keep in mind that the significance of each IV is calculated after accounting for the variance of all the other variables in the model, assuming you’re using the standard adjusted sums of squares rather than sequential sums of squares. The sums of squares (SS) is a measure of how much dependent variable variability that each IV accounts for. In the illustration below, I’ll assume you’re using the standard of adjusted SS.
So, let’s say that originally you have X1 in the model along with some other IVs. Your model estimates the significance of X1 after assessing the variability that the other IVs account for and finds that X1 is significant. Now, you add X2 to the model in addition to X1 and the other IVs. Now, when assessing X1, the model accounts for the variability of the IVs including the newly added X2. And apparently X2 explains a good portion of the variability. X1 is no longer able to account for that variability, which causes it to not be statistically significant.
In other words, X2 explains some of the variability that X1 previously explained. Because X1 no longer explains it, it is no longer significant.
Additionally, the significance of IVs is more likely to change when you add or remove IVs that are correlated. Correlated IVs is known as multicollinearity. Multicollinearity can be a problem when you have too much. Given the change in significance, I’d check your model for multicollinearity just to be safe! Click the link to read a post that wrote about that!
September 6, 2021 at 8:35 am
nice explanation
August 25, 2021 at 3:09 am
it is excellent explanation
Comments and Questions Cancel reply
Plant Breeding and Genomics
Introduction to Experimental Design
Shawn C. Yarnes, The Ohio State University
Defining Variables and Experimental Units
Experimental design begins with the formulation of experimental questions , which help define the variables that will change in an experiment. Experimental treatments , or independent variables , are the controlled part of an experiment expected to affect the response , or dependent variables . The experimenter must identify which treatment and response variables will best answer experimental questions.
Consider the broad experimental question. How do plants respond to fertilizer application? This question must be made more specific to design an effective experiment.
The dependent variable , plant response , can be defined and measured in numerous ways. If the experimenter is interested in plant growth and nitrogen content, the question can be made more specific by asking how does plant growth and nitrogen content change in response to fertilizer application? Determination of response variables is influenced by experimental objectives and practical considerations. For example, total dry weight is more accurate than height as a measurement of plant growth, but in the case of a tree experiment, height might be more practical.
The independent variable , fertilizer treatment , can also be defined in numerous ways that will help specify experimental questions. A single fertilizer treatment with different levels can be tested, or multiple fertilizers compared. Levels can be: qualitative, or categorical, as when denoting males and females in a population; or quantitative, such as different fertilizer concentrations. Levels can also be defined as fixed or random effects. Sex distribution in a population is generally a random effect ; while fertilizer application is an experimenter controlled, or fixed effect . The decision to define a variable as fixed or random will affect future statistical analyses (See Analysis of Variance (ANOVA): Experimental Design for Fixed and Random Effects ).
Once response and experimental treatments are defined, proper control treatments must be determined. Controls are integral to the scientific method by providing baseline values against which other treatments are compared. Negative controls , such as nonfertilized plants in Example 1, are null treatments where no response is expected. The simplest experiment has one response variable, one negative control, and one treatment. If experimental results support a null hypothesis (H 0 ), no significant difference is observed between controls and other treatments.
Positive controls are treatments where a known response is expected. Positive controls are often used to validate assays or equipment functioning. For example, many enzyme kits come with predigested substrates, so that experimental digestions can be deemed successful compared to the positive control. Positive controls can also be used to calibrate or standardize measurements. For example, a standard curve of known substrate concentrations can be used to calculate the amount of unknown substrate concentrations.
Experimental units must be defined during experimental design. The experimental unit is an individual, object, or plot subjected to treatment independently of other units. The number of experimental units is the sum of all treatments, levels, and and replicates. When experimental units are sampled only once, the experimental unit and sampling unit are the same. The experimental unit can also be comprised of multiple sampling units. When experimental units are heterogeneous for the response variable, the mean of multiple sample units can be more precise than a single measure. For example, if leaf nitrogen content is variable between leaves, an experimenter may choose to measure the nitrogen content from multiple leaves, using the mean nitrogen content to represent the individual plant. Increasing the sampling units does not increase replication.
Planning for Statistical Inference
The goal of an experiment is to detect differences between treatments. Statistical determination of these differences requires replication to compute experimental error and randomization to help ensure that the measure of experimental error is valid. Discussions of experimental error and replication become circular, because replications are needed to compute experimental error, and the number of replications needed is based on the magnitude of experimental error. Experimental design requires an a priori estimation of error. In some situations a preliminary study is used to estimate error. In other situations error is inferred using reasonable assumptions based on the current understanding of the study system.
Experimental Error
Experimental error is the variation among experimental units within the same treatment group. There are many possible reasons for error. Errors within an experiment are additive. Reducing the amount of error in an experiment increases your ability to detect significant differences between treatments. A welldesigned experiment considers the error contributed by both natural variation and lack of experimental uniformity.
Natural variation is a large component of error in biological experiments. Genetic and developmental differences, as well as differences in species abundance and diversity, can vary between experimental units. In plant breeding, clones and inbreed lines are often utilized to reduce genetic variation between experimental units.
Lack of experimental uniformity is the source of error over which an investigator has the most control. Although there is always an imperfect ability to provide identical environments for each experimental unit, identifying and controlling error is essential. Errors in technique and/or data recording can inflate estimated experimental error (decrease precision) and introduce bias into the results (decrease accuracy).
Relationship Between Error and Sample Size
The sample size needed to detect differences between treatments increases with error. This is the reason biological field experiments generally require larger sample sizes than more controlled laboratory experiments. Experimental effort and expense are directly proportional to sample size. For these reasons controlling error is the focus of every investigator.
The graph below illustrates the realtionship between error (σ), sample size, and the ability to detect differences between two means. (See Estimating Sample Size for Comparison of Two Means and Equation to Estimate Sample Size Required for QTL Detection ).
Funding Statement
Development of this page was supported in part by the National Institute of Food and Agriculture (NIFA) Solanaceae Coordinated Agricultural Project, agreement 20098560605673, administered by Michigan State University. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the United States Department of Agriculture.
PBGworks 1445
PBG Content Committee
 Introduction to Experimental Design
Shawn C. Yarnes, The Ohio State University
Defining Variables and Experimental Units
Experimental design begins with the formulation of experimental questions , which help define the variables that will change in an experiment. Experimental treatments , or independent variables , are the controlled part of an experiment expected to affect the response , or dependent variables . The experimenter must identify which treatment and response variables will best answer experimental questions.
Consider the broad experimental question. How do plants respond to fertilizer application? This question must be made more specific to design an effective experiment.
The dependent variable , plant response , can be defined and measured in numerous ways. If the experimenter is interested in plant growth and nitrogen content, the question can be made more specific by asking how does plant growth and nitrogen content change in response to fertilizer application? Determination of response variables is influenced by experimental objectives and practical considerations. For example, total dry weight is more accurate than height as a measurement of plant growth, but in the case of a tree experiment, height might be more practical.
The independent variable , fertilizer treatment , can also be defined in numerous ways that will help specify experimental questions. A single fertilizer treatment with different levels can be tested, or multiple fertilizers compared. Levels can be: qualitative, or categorical, as when denoting males and females in a population; or quantitative, such as different fertilizer concentrations. Levels can also be defined as fixed or random effects. Sex distribution in a population is generally a random effect ; while fertilizer application is an experimenter controlled, or fixed effect . The decision to define a variable as fixed or random will affect future statistical analyses (See Analysis of Variance (ANOVA): Experimental Design for Fixed and Random Effects ).
Once response and experimental treatments are defined, proper control treatments must be determined. Controls are integral to the scientific method by providing baseline values against which other treatments are compared. Negative controls , such as nonfertilized plants in Example 1, are null treatments where no response is expected. The simplest experiment has one response variable, one negative control, and one treatment. If experimental results support a null hypothesis (H 0 ), no significant difference is observed between controls and other treatments.
Positive controls are treatments where a known response is expected. Positive controls are often used to validate assays or equipment functioning. For example, many enzyme kits come with predigested substrates, so that experimental digestions can be deemed successful compared to the positive control. Positive controls can also be used to calibrate or standardize measurements. For example, a standard curve of known substrate concentrations can be used to calculate the amount of unknown substrate concentrations.
Experimental units must be defined during experimental design. The experimental unit is an individual, object, or plot subjected to treatment independently of other units. The number of experimental units is the sum of all treatments, levels, and and replicates. When experimental units are sampled only once, the experimental unit and sampling unit are the same. The experimental unit can also be comprised of multiple sampling units. When experimental units are heterogeneous for the response variable, the mean of multiple sample units can be more precise than a single measure. For example, if leaf nitrogen content is variable between leaves, an experimenter may choose to measure the nitrogen content from multiple leaves, using the mean nitrogen content to represent the individual plant. Increasing the sampling units does not increase replication.
Planning for Statistical Inference
The goal of an experiment is to detect differences between treatments. Statistical determination of these differences requires replication to compute experimental error and randomization to help ensure that the measure of experimental error is valid. Discussions of experimental error and replication become circular, because replications are needed to compute experimental error, and the number of replications needed is based on the magnitude of experimental error. Experimental design requires an a priori estimation of error. In some situations a preliminary study is used to estimate error. In other situations error is inferred using reasonable assumptions based on the current understanding of the study system.
Experimental Error
Experimental error is the variation among experimental units within the same treatment group. There are many possible reasons for error. Errors within an experiment are additive. Reducing the amount of error in an experiment increases your ability to detect significant differences between treatments. A welldesigned experiment considers the error contributed by both natural variation and lack of experimental uniformity.
Natural variation is a large component of error in biological experiments. Genetic and developmental differences, as well as differences in species abundance and diversity, can vary between experimental units. In plant breeding, clones and inbreed lines are often utilized to reduce genetic variation between experimental units.
Lack of experimental uniformity is the source of error over which an investigator has the most control. Although there is always an imperfect ability to provide identical environments for each experimental unit, identifying and controlling error is essential. Errors in technique and/or data recording can inflate estimated experimental error (decrease precision) and introduce bias into the results (decrease accuracy).
Relationship Between Error and Sample Size
The sample size needed to detect differences between treatments increases with error. This is the reason biological field experiments generally require larger sample sizes than more controlled laboratory experiments. Experimental effort and expense are directly proportional to sample size. For these reasons controlling error is the focus of every investigator.
The graph below illustrates the realtionship between error (σ), sample size, and the ability to detect differences between two means. (See Estimating Sample Size for Comparison of Two Means and Equation to Estimate Sample Size Required for QTL Detection ).
Funding Statement
Development of this page was supported in part by the National Institute of Food and Agriculture (NIFA) Solanaceae Coordinated Agricultural Project, agreement 20098560605673, administered by Michigan State University. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the United States Department of Agriculture.
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 Activities, Experiments, Online Games, Visual Aids
 Activities, Experiments, and Investigations
 Experimental Design and the Scientific Method
Experimental Design  Independent, Dependent, and Controlled Variables
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Scientific experiments are meant to show cause and effect of a phenomena (relationships in nature). The “ variables ” are any factor, trait, or condition that can be changed in the experiment and that can have an effect on the outcome of the experiment.
An experiment can have three kinds of variables: i ndependent, dependent, and controlled .
 The independent variable is one single factor that is changed by the scientist followed by observation to watch for changes. It is important that there is just one independent variable, so that results are not confusing.
 The dependent variable is the factor that changes as a result of the change to the independent variable.
 The controlled variables (or constant variables) are factors that the scientist wants to remain constant if the experiment is to show accurate results. To be able to measure results, each of the variables must be able to be measured.
For example, let’s design an experiment with two plants sitting in the sun side by side. The controlled variables (or constants) are that at the beginning of the experiment, the plants are the same size, get the same amount of sunlight, experience the same ambient temperature and are in the same amount and consistency of soil (the weight of the soil and container should be measured before the plants are added). The independent variable is that one plant is getting watered (1 cup of water) every day and one plant is getting watered (1 cup of water) once a week. The dependent variables are the changes in the two plants that the scientist observes over time.
Can you describe the dependent variable that may result from this experiment? After four weeks, the dependent variable may be that one plant is taller, heavier and more developed than the other. These results can be recorded and graphed by measuring and comparing both plants’ height, weight (removing the weight of the soil and container recorded beforehand) and a comparison of observable foliage.
Using What You Learned: Design another experiment using the two plants, but change the independent variable. Can you describe the dependent variable that may result from this new experiment?
Think of another simple experiment and name the independent, dependent, and controlled variables. Use the graphic organizer included in the PDF below to organize your experiment's variables.
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Methodology
 Independent vs. Dependent Variables  Definition & Examples
Independent vs. Dependent Variables  Definition & Examples
Published on February 3, 2022 by Pritha Bhandari . Revised on June 22, 2023.
In research, variables are any characteristics that can take on different values, such as height, age, temperature, or test scores.
Researchers often manipulate or measure independent and dependent variables in studies to test causeandeffect relationships.
 The independent variable is the cause. Its value is independent of other variables in your study.
 The dependent variable is the effect. Its value depends on changes in the independent variable.
Your independent variable is the temperature of the room. You vary the room temperature by making it cooler for half the participants, and warmer for the other half.
Table of contents
What is an independent variable, types of independent variables, what is a dependent variable, identifying independent vs. dependent variables, independent and dependent variables in research, visualizing independent and dependent variables, other interesting articles, frequently asked questions about independent and dependent variables.
An independent variable is the variable you manipulate or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.
Independent variables are also called:
 Explanatory variables (they explain an event or outcome)
 Predictor variables (they can be used to predict the value of a dependent variable)
 Righthandside variables (they appear on the righthand side of a regression equation).
These terms are especially used in statistics , where you estimate the extent to which an independent variable change can explain or predict changes in the dependent variable.
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There are two main types of independent variables.
 Experimental independent variables can be directly manipulated by researchers.
 Subject variables cannot be manipulated by researchers, but they can be used to group research subjects categorically.
Experimental variables
In experiments, you manipulate independent variables directly to see how they affect your dependent variable. The independent variable is usually applied at different levels to see how the outcomes differ.
You can apply just two levels in order to find out if an independent variable has an effect at all.
You can also apply multiple levels to find out how the independent variable affects the dependent variable.
You have three independent variable levels, and each group gets a different level of treatment.
You randomly assign your patients to one of the three groups:
 A lowdose experimental group
 A highdose experimental group
 A placebo group (to research a possible placebo effect )
A true experiment requires you to randomly assign different levels of an independent variable to your participants.
Random assignment helps you control participant characteristics, so that they don’t affect your experimental results. This helps you to have confidence that your dependent variable results come solely from the independent variable manipulation.
Subject variables
Subject variables are characteristics that vary across participants, and they can’t be manipulated by researchers. For example, gender identity, ethnicity, race, income, and education are all important subject variables that social researchers treat as independent variables.
It’s not possible to randomly assign these to participants, since these are characteristics of already existing groups. Instead, you can create a research design where you compare the outcomes of groups of participants with characteristics. This is a quasiexperimental design because there’s no random assignment. Note that any research methods that use nonrandom assignment are at risk for research biases like selection bias and sampling bias .
Your independent variable is a subject variable, namely the gender identity of the participants. You have three groups: men, women and other.
Your dependent variable is the brain activity response to hearing infant cries. You record brain activity with fMRI scans when participants hear infant cries without their awareness.
A dependent variable is the variable that changes as a result of the independent variable manipulation. It’s the outcome you’re interested in measuring, and it “depends” on your independent variable.
In statistics , dependent variables are also called:
 Response variables (they respond to a change in another variable)
 Outcome variables (they represent the outcome you want to measure)
 Lefthandside variables (they appear on the lefthand side of a regression equation)
The dependent variable is what you record after you’ve manipulated the independent variable. You use this measurement data to check whether and to what extent your independent variable influences the dependent variable by conducting statistical analyses.
Based on your findings, you can estimate the degree to which your independent variable variation drives changes in your dependent variable. You can also predict how much your dependent variable will change as a result of variation in the independent variable.
Distinguishing between independent and dependent variables can be tricky when designing a complex study or reading an academic research paper .
A dependent variable from one study can be the independent variable in another study, so it’s important to pay attention to research design .
Here are some tips for identifying each variable type.
Recognizing independent variables
Use this list of questions to check whether you’re dealing with an independent variable:
 Is the variable manipulated, controlled, or used as a subject grouping method by the researcher?
 Does this variable come before the other variable in time?
 Is the researcher trying to understand whether or how this variable affects another variable?
Recognizing dependent variables
Check whether you’re dealing with a dependent variable:
 Is this variable measured as an outcome of the study?
 Is this variable dependent on another variable in the study?
 Does this variable get measured only after other variables are altered?
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Independent and dependent variables are generally used in experimental and quasiexperimental research.
Here are some examples of research questions and corresponding independent and dependent variables.
Research question  Independent variable  Dependent variable(s) 

Do tomatoes grow fastest under fluorescent, incandescent, or natural light?  
What is the effect of intermittent fasting on blood sugar levels?  
Is medical marijuana effective for pain reduction in people with chronic pain?  
To what extent does remote working increase job satisfaction? 
For experimental data, you analyze your results by generating descriptive statistics and visualizing your findings. Then, you select an appropriate statistical test to test your hypothesis .
The type of test is determined by:
 your variable types
 level of measurement
 number of independent variable levels.
You’ll often use t tests or ANOVAs to analyze your data and answer your research questions.
In quantitative research , it’s good practice to use charts or graphs to visualize the results of studies. Generally, the independent variable goes on the x axis (horizontal) and the dependent variable on the y axis (vertical).
The type of visualization you use depends on the variable types in your research questions:
 A bar chart is ideal when you have a categorical independent variable.
 A scatter plot or line graph is best when your independent and dependent variables are both quantitative.
To inspect your data, you place your independent variable of treatment level on the x axis and the dependent variable of blood pressure on the y axis.
You plot bars for each treatment group before and after the treatment to show the difference in blood pressure.
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
 Normal distribution
 Degrees of freedom
 Null hypothesis
 Discourse analysis
 Control groups
 Mixed methods research
 Nonprobability sampling
 Quantitative research
 Ecological validity
Research bias
 Rosenthal effect
 Implicit bias
 Cognitive bias
 Selection bias
 Negativity bias
 Status quo bias
An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.
A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.
In statistics, dependent variables are also called:
Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.
You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .
 The type of soda – diet or regular – is the independent variable .
 The level of blood sugar that you measure is the dependent variable – it changes depending on the type of soda.
No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!
Yes, but including more than one of either type requires multiple research questions .
For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.
You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .
To ensure the internal validity of an experiment , you should only change one independent variable at a time.
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Dependent vs. Independent Variables in Research
Introduction
Independent and dependent variables in research, can qualitative data have independent and dependent variables.
Experiments rely on capturing the relationship between independent and dependent variables to understand causal patterns. Researchers can observe what happens when they change a condition in their experiment or if there is any effect at all.
It's important to understand the difference between the independent variable and dependent variable. We'll look at the notion of independent and dependent variables in this article. If you are conducting experimental research, defining the variables in your study is essential for realizing rigorous research .
In experimental research, a variable refers to the phenomenon, person, or thing that is being measured and observed by the researcher. A researcher conducts a study to see how one variable affects another and make assertions about the relationship between different variables.
A typical research question in an experimental study addresses a hypothesized relationship between the independent variable manipulated by the researcher and the dependent variable that is the outcome of interest presumably influenced by the researcher's manipulation.
Take a simple experiment on plants as an example. Suppose you have a control group of plants on one side of a garden and an experimental group of plants on the other side. All things such as sunlight, water, and fertilizer being equal, both plants should be expected to grow at the same rate.
Now imagine that the plants in the experimental group are given a new plant fertilizer under the assumption that they will grow faster. Then you will need to measure the difference in growth between the two groups in your study.
In this case, the independent variable is the type of fertilizer used on your plants while the dependent variable is the rate of growth among your plants. If there is a significant difference in growth between the two groups, then your study provides support to suggest that the fertilizer causes higher rates of plant growth.
What is the key difference between independent and dependent variables?
The independent variable is the element in your study that you intentionally change, which is why it can also be referred to as the manipulated variable.
You manipulate this variable to see how it might affect the other variables you observe, all other factors being equal. This means that you can observe the cause and effect relationships between one independent variable and one or multiple dependent variables.
Independent variables are directly manipulated by the researcher, while dependent variables are not. They are "dependent" because they are affected by the independent variable in the experiment. Researchers can thus study how manipulating the independent variable leads to changes in the main outcome of interest being measured as the dependent variable.
Note that while you can have multiple dependent variables, it is challenging to establish research rigor for multiple independent variables. If you are making so many changes in an experiment, how do you know which change is responsible for the outcome produced by the study? Studying more than one independent variable would require running an experiment for each independent variable to isolate its effects on the dependent variable.
This being said, it is certainly possible to employ a study design that involves multiple independent and dependent variables, as is the case with what is called a factorial experiment. For example, a psychological study examining the effects of sleep and stress levels on work productivity and social interaction would have two independent variables and two dependent variables, respectively.
Such a study would be complex and require careful planning to establish the necessary research rigor , however. If possible, consider narrowing your research to the examination of one independent variable to make it more manageable and easier to understand.
Independent variable examples
Let's consider an experiment in the social studies. Suppose you want to determine the effectiveness of a new textbook compared to current textbooks in a particular school.
The new textbook is supposed to be better, but how can you prove it? Besides all the selling points that the textbook publisher makes, how do you know if the new textbook is any good? A rigorous study examining the effects of the textbook on classroom outcomes is in order.
The textbook given to students makes up the independent variable in your experimental study. The shift from the existing textbooks to the new one represents the manipulation of the independent variable in this study.
Dependent variable examples
In any experiment, the dependent variable is observed to measure how it is affected by changes to the independent variable. Outcomes such as test scores and other performance metrics can make up the data for the dependent variable.
Now that we are changing the textbook in the experiment above, we should examine if there are any effects.
To do this, we will need two classrooms of students. As best as possible, the two sets of students should be of similar proficiency (or at least of similar backgrounds) and placed within similar conditions for teaching and learning (e.g., physical space, lesson planning).
The control group in our study will be one set of students using the existing textbook. By examining their performance, we can establish a baseline. The performance of the experimental group, which is the set of students using the new textbook, can then be compared with the baseline performance.
As a result, the change in the test scores make up the data for our dependent variable. We cannot directly affect how well students perform on the test, but we can conclude from our experiment whether the use of the new textbook might impact students' performance.
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How do you know if a variable is independent or dependent?
We can typically think of an independent variable as something a researcher can directly change. In the above example, we can change the textbook used by the teacher in class. If we're talking about plants, we can change the fertilizer.
Conversely, the dependent variable is something that we do not directly influence or manipulate. Strictly speaking, we cannot directly manipulate a student's performance on a test or the rate of growth of a plant, not without other factors such as new teaching methods or new fertilizer, respectively.
Understanding the distinction between a dependent variable and an independent variable is key to experimental research. Ultimately, the distinction can be reduced to which element in a study has been directly influenced by the researcher.
Other variables
Given the potential complexities encountered in research, there is essential terminology for other variables in any experimental study. You might employ this terminology or encounter them while reading other research.
A control variable is any factor that the researcher tries to keep constant as the independent variable changes. In the plant experiment described earlier in this article, the sunlight and water are each a controlled variable while the type of fertilizer used is the manipulated variable across control and experimental groups.
To ensure research rigor, the researcher needs to keep these control variables constant to dispel any concerns that differences in growth rate were being driven by sunlight or water, as opposed to the fertilizer being used.
Extraneous variables refer to any unwanted influence on the dependent variable that may confound the analysis of the study. For example, if bugs or animals ate the plants in your fertilizer study, this was greatly impact the rates of plant growth. This is why it would be important to control the environment and protect it from such threats.
Finally, independent variables can go by different names such as subject variables or predictor variables. Dependent variables can also be referred to as the responding variable or outcome variable. Whatever the language, they all serve the same role of influencing the dependent variable in an experiment.
The use of the word " variables " is typically associated with quantitative and confirmatory research. Naturalistic qualitative research typically does not employ experimental designs or establish causality. Qualitative research often draws on observations , interviews , focus groups , and other forms of data collection that are allow researchers to study the naturally occurring "messiness" of the social world, rather than controlling all variables to isolate a causeandeffect relationship.
In limited circumstances, the idea of experimental variables can apply to participant observations in ethnography , where the researcher should be mindful of their influence on the environment they are observing.
However, the experimental paradigm is best left to quantitative studies and confirmatory research questions. Qualitative researchers in the social sciences are oftentimes more interested in observing and describing sociallyconstructed phenomena rather than testing hypotheses .
Nonetheless, the notion of independent and dependent variables does hold important lessons for qualitative researchers. Even if they don't employ variables in their study design, qualitative researchers often observe how one thing affects another. A theoretical or conceptual framework can then suggest potential causeandeffect relationships in their study.
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1.13: Experiment
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So what exactly is an experiment?
At first you may picture a science laboratory with microscopes and chemicals and people in white lab coats. But do all experiments have to be done in a lab? And do all scientists have to wear lab coats?
Experiments
Figure below shows a laboratory experiment involving plants. An experiment is a special type of scientific investigation that is performed under controlled conditions, usually in a laboratory .
Some experiments can be very simple, but even the simplest can contribute important evidence that helps scientists better understand the natural world.
As many different types of experiments are possible, an experiment must be designed to produce data that can help confirm or reject the hypothesis .
An experiment generally tests how one variable is affected by another. The affected variable is called the dependent variable . In the plant experiment shown above, the dependent variable is plant growth. The variable that affects the dependent variable is called the independent variable . In the plant experiment, the independent variable could be fertilizer—some plants will get fertilizer, others will not. The scientists change the amount of the independent variable (the fertilizer) to observe the effects on the dependent variable (plant growth). An experiment needs to be run simultaneously in which no fertilizer is given to the plant. This would be known as a control experiment. In any experiment, other factors that might affect the dependent variable must be controlled. In the plant experiment, what factors do you think should be controlled? ( Hint: What other factors might affect plant growth?)
Sample Size and Repetition
The sample in an experiment or other investigation consists of the individuals or events that are studied, and the size of the sample (or sample size ) directly affects the interpretation of the results. Typically, the sample is much smaller than all such individuals or events that exist in the world. Whether the results based on the sample are true in general cannot be known for certain. However, the larger the sample is, the more likely it is that the results are generally true.
Similarly, the more times that an experiment is repeated (which is known as repetition ) and the same results obtained, the more likely the results are valid. This is why scientific experiments should always be repeated.
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Microscopes are arguably one of the most important tools of the biologist. They allow the visualization of smaller and smaller biological organisms and molecules. With greatly magnified powers, these instruments are becoming increasingly important in modern day research.
Science Friday: The Lollipop Hypothesis
Ever wondered how many licks it takes to reach the center of a lollipop? Mathematicians at NYU’s applied mathematics lab have designed experiments to determine this. Find out in this video by Science Friday.
Science Friday: No Strain, No Gain: Filter Feeding Mantas
Mantas are an example of filter feeders that obtain food as they swim through the water . How do these filters work? In this video by Science Friday, Dr. Misty PaigTran discusses the experiments she performed to understand these filters.
 An experiment is a special type of scientific investigation that is performed under controlled conditions, usually in a laboratory.
 An experiment generally tests how one variable is affected by another.
 The sample size in an experiment directly affects the interpretation of the results.
 Repetition is the repeating of an experiment, validating the results.
 What is an experiment?
 Compare the dependent variable to the independent variable.
 Identify the independent and dependent variables in the following experiment: A scientist grew bacteria on gel in her lab. She wanted to find out if the bacteria would grow faster on gel A or gel B. She placed a few bacteria on gel A and a few on gel B. After 24 hours, she observed how many bacteria were present on each type of gel.
Eric Schmelz, U.S. Department of Agriculture;NIAID Research ; ;  
Eric Schmelz, U.S. Department of Agriculture  
NIAID;Eric Schmelz, U.S. Department of Agriculture ; 
Independent variable
An independent variable is a type of variable that is used in mathematics, statistics, and the experimental sciences. It is the variable that is manipulated in order to determine whether it has an effect on the dependent variable .
Real world examples of independent variables include things like fertilizer given to plants, where the dependent variable may be plant height; medication, where one group gets a placebo and the other gets the medication, and the dependent variable may be their health outcomes; the amount of caffeine a person drinks, where the dependent variable may be the number of hours they sleep.
Independent variables in algebra
In algebra, independent variables are usually discussed in the context of equations and functions. Most commonly, the independent variable is "x," (though others, such as t for time, are used as well) as in the equation
or in function notation:
f(x) = x + 5
In the above, x is the independent variable because it is the variable that we control. Depending on what value of x is plugged into the function, f(x) (or y) changes. As such, it is common to characterize the independent variable as the input of a function, while the dependent variable is the output.
Referencing the above example, if the independent variable, x, is equal to 5, we can write this in function notation as f(5), and can compute the dependent variable as follows:
f(5) = 5 + 5 = 10
In this function, f(x) is always 5 more than x.
In graphs, independent variables are graphed along the xaxis, and dependent variables are graphed along the yaxis:
It is possible for a function to have multiple independent and dependent variables, though this is more common in higher mathematics, not algebra.
Independent variables in experiments
In the context of statistics and experiments, the independent variable is the control. It is the known variable that is manipulated, while the dependent variable is the variable that is expected to change as a result of manipulating the independent variable. In an experiment, the goal is typically to determine whether the independent variable has any effect on the dependent variable, and if so, how it affects the dependent variable. It follows that an independent variable may also be referred to as the explanatory variable, manipulated variable, and predictor variable, among other things. Similarly, a dependent variable may be referred to as the explained variable, response variable, predicted variable, and so on.
As an example, in an experiment that measures the growth of a group of plants that are given varying amounts of fertilizer, the independent variable is the amount of fertilizer administered, and the dependent variable is the growth of the plant. Adding more fertilizer might increase (or decrease) the growth of the plant. However, the growth of the plant will not directly affect the amount of fertilizer added.
Statistics Made Easy
What Are Levels of an Independent Variable?
In an experiment, there are two types of variables:
The independent variable: The variable that an experimenter changes or controls so that they can observe the effects on the dependent variable.
The dependent variable: The variable being measured in an experiment that is “dependent” on the independent variable.
In an experiment, a researcher wants to understand how changes in an independent variable affect a dependent variable.
When an independent variable has multiple experimental conditions, we say that there are levels of the independent variable .
For example, suppose a teacher wants to know how three different studying techniques affect exam scores. She randomly assigns 30 students each to use one of the three studying techniques for a week, then each student takes the exact same exam.
In this example, the independent variable is Studying Technique and it has three levels :
 Technique 1
 Technique 2
 Technique 3
In other words, there are the three experimental conditions that the students can potentially be exposed to.
The dependent variable in this example is Exam Score, which is “dependent” on the studying technique used by the student.
The following examples illustrate a few more experiments that use independent variables with multiple levels.
Example 1: Advertising Spend
Suppose a marketer conducts an experiment in which he spends three different amounts of money (low, medium, high) on TV advertising to see how it affects the sales of a certain product.
In this experiment, we have the following variables:
Independent Variable: Advertising Spend
Dependent Variable: Total sales of the product
Example 2: Placebo vs. Medication
Suppose a doctor wants to know if a certain medication reduces blood pressure in patients. He recruits a simple random sample of 100 patients and randomly assigns 50 to use a pill that contains the real medication and 50 to use a pill that is actually just a placebo.
Independent Variable: Type of Medication
 True medication pill
 Placebo pill
Dependent Variable: Overall change in blood pressure
Example 3: Plant Growth
Suppose a botanist uses five different fertilizers (We’ll call them A, B, C, D, E) in a field to determine if they have different effects on plant growth.
Independent Variable: Type of fertilizer
 Fertilizer A
 Fertilizer B
 Fertilizer C
 Fertilizer D
 Fertilizer E
Dependent Variable: Plant growth
How to Analyze Levels of an Independent Variable
Typically we use a oneway ANOVA to determine if the levels of an independent variable cause different outcomes in a dependent variable.
A oneway ANOVA uses the following null and alternative hypotheses:
 H 0 (null): All group means are equal
 H 1 (alternative): At least one group mean is different from the rest
For example, we could use a oneway ANOVA to determine if the five different types of fertilizer in the previous example lead to different mean growth rates for the plants.
If the pvalue of the ANOVA is less than some significance level (e.g. α = .05), then we can reject the null hypothesis. This means we have sufficient evidence to say that the mean plant growth is not equal at all five levels of the fertilizer.
We could then proceed to conduct posthoc tests to determine exactly which fertilizers lead to different mean growth rates.
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What Is The Independent Variable In A Plant Growth Experiment
In the realm of scientific research, understanding the variables at play is crucial to unraveling the intricacies of experiments. One fundamental and influential variable within plant growth experiments is the independent variable. Defined as the condition or factor manipulated by the researchers, the independent variable holds the power to shape the course of the experiment and ultimately affect the growth of plants. It serves as a gateway to unlocking valuable insights into the intricate world of botanical development. To comprehend the role and significance of the independent variable in plant growth experiments, it is essential to delve into its characteristics and examine its implications within this scientific domain.
The independent variable, often referred to as the manipulated variable, is the key element carefully selected and adjusted by researchers to explore its potential impact on plant growth. It is important to grasp that the independent variable is intentionally altered to assess its effects on the dependent variable, which represents the outcome being measured or observed. By modifying the independent variable, researchers have the opportunity to study the causeandeffect relationship it has with plant growth, ultimately providing a deeper understanding of these organisms’ intricate mechanisms.
The selection and refinement of the independent variable demand careful consideration. Its choice should be driven by a clear and focused research question or hypothesis, allowing researchers to investigate specific factors that may influence plant growth. For instance, an independent variable in a plant growth experiment could be varying levels of sunlight exposure, different concentrations of nutrients in the soil, or contrasting irrigation techniques. By manipulating these variables, scientists gain valuable insights into the correlation between their alterations and subsequent effects on plant growth.
Moreover, it is important to note that a single experiment can incorporate multiple independent variables, though each one should be analyzed and treated separately to accurately assess their individual influence on plant growth. For instance, by simultaneously altering water levels and temperature, researchers can assess the distinct impacts of both variables, contributing to a more comprehensive understanding of the factors driving plant development. However, it is essential to ensure that the experimental design allows for isolation of the effects of each independent variable, enabling accurate interpretations of the results.
By manipulating the independent variable within plant growth experiments, scientists unlock the potential to explore and unravel the complex relationship between various factors and the growth of plants. Through a careful selection, adjustment, and isolation of the independent variable, researchers can provide valuable insights into botanical development. Consequently, understanding the role and significance of the independent variable serves as an essential foundation for not only comprehending plant growth but also contributing to future advancements in agriculture, horticulture, and ecological studies.
key Takeaways
 The independent variable in a plant growth experiment is the variable that is manipulated or changed by the researcher.
 It is the factor that the researcher believes will have an effect on the dependent variable, which is the outcome or result of the experiment.
 In a plant growth experiment, examples of independent variables could include the amount of water given to the plants, the type of fertilizer used, or the amount of light exposure.
 The independent variable is typically presented in different levels or conditions, allowing the researcher to compare the effects of each level on the dependent variable.
 Controlling all other variables except the independent variable is crucial in order to accurately determine its impact on plant growth.
 Randomization is important when assigning plants to different levels of the independent variable to minimize bias and ensure the validity of the experiment.
 The independent variable should be clearly defined and accurately measured to ensure consistency and reproducibility of the experiment.
 The results of a plant growth experiment can provide valuable insights into optimal conditions for plant growth and inform agricultural practices.
Defining the Independent Variable in a Plant Growth Experiment
In order to accurately conduct and analyze any scientific experiment, it is crucial to understand the concept of the independent variable. When it comes to a plant growth experiment, the independent variable plays a key role in determining the outcome and understanding the factors that influence plant growth.
Understanding the Independent Variable
The independent variable refers to the factor or condition that is intentionally manipulated or changed by the researcher in an experiment. It is the variable that the researcher believes will have an effect on the dependent variable, which is the variable being measured or observed in response to the changes made to the independent variable.
In the context of a plant growth experiment, the independent variable refers to the factor that is being altered to examine its impact on the growth of the plants. This variable can be any aspect that the researcher wants to investigate, such as the type of fertilizer used, the amount of water provided, the intensity and duration of light exposure, or the presence of certain chemicals.
Significance of the Independent Variable
The independent variable is crucial for establishing causeandeffect relationships in scientific experiments. By manipulating and controlling the independent variable, researchers can determine whether any observed changes in the dependent variable are a direct result of the manipulated factor, or if they are influenced by other variables.
In a plant growth experiment, identifying and effectively manipulating the independent variable allows researchers to understand how specific conditions or factors affect the growth and development of plants. By varying one factor at a time while keeping all other variables constant, researchers can pinpoint the impact of each independent variable on the plants, leading to valuable insights and conclusions.
Examples of Independent Variables in a Plant Growth Experiment
There are numerous independent variables that researchers can explore in plant growth experiments. Some common examples include:
 Type of Fertilizer: Examining how different types of fertilizers, such as organic or synthetic ones, affect plant growth.
 Amount of Water: Investigating the impact of varying watering schedules or quantities of water on plant growth.
 Light Exposure: Studying how different light intensities, durations, or wavelengths affect the growth and development of plants.
 Presence of Chemicals: Analyzing the effects of specific chemicals, such as pesticides or growth hormones, on plant growth.
By selecting and manipulating one independent variable at a time, researchers can uncover the relationship between that variable and the growth of plants, contributing to a better understanding of plant biology and facilitating advancements in agriculture and horticulture.
Frequently Asked Questions
What is the independent variable in a plant growth experiment.
The independent variable in a plant growth experiment is the variable that is manipulated or changed by the researcher. It is the factor that is believed to have an impact on the growth of the plants being studied. It is typically represented on the xaxis of a graph.
Why is the independent variable important in a plant growth experiment?
The independent variable is important in a plant growth experiment because it allows researchers to test the effects of different factors on the growth of plants. By manipulating the independent variable, researchers can determine if there is a causal relationship between the variable and the plant’s growth. This information is essential for understanding how certain factors affect plant growth and can inform agricultural practices and plant breeding techniques.
What are some examples of independent variables in plant growth experiments?
Some examples of independent variables in plant growth experiments may include the amount of water given to the plants, the type of fertilizer used, the intensity of light exposure, or the temperature in which the plants are grown. These variables can be systematically manipulated to see how they affect the growth of the plants being studied.
How is the independent variable determined in a plant growth experiment?
The determination of the independent variable in a plant growth experiment depends on the research question or hypothesis being investigated. The researcher needs to identify the factor that they believe may have an impact on plant growth and then set up experimental conditions to test the effects of varying levels or conditions of that factor.
Can there be more than one independent variable in a plant growth experiment?
Yes, there can be more than one independent variable in a plant growth experiment. In some studies, researchers may be interested in examining the effects of multiple factors on plant growth simultaneously. In these cases, multiple independent variables would be manipulated and studied to understand their individual and combined effects.
The Different Types and Options for Plant Growth Experiments
Types of plant growth experiments.
There are several types of plant growth experiments that researchers may choose to conduct, depending on their specific research question or objective. These types include comparative experiments, control experiments, factorial experiments, and field experiments.
Comparative experiments
In a comparative experiment, researchers compare the growth of plants under different conditions or treatments. This allows them to determine the effects of specific variables on the growth of the plants.
Control experiments
A control experiment involves setting up a control group that is kept under standard or normal conditions, while other groups are subjected to different treatments. The control group serves as a baseline for comparison and allows researchers to isolate the effects of the independent variables being tested.
Factorial experiments
Factorial experiments involve manipulating more than one independent variable simultaneously. This allows researchers to analyze the effects of each variable individually, as well as their interactions.
Field experiments
Field experiments are conducted in natural environments, such as farms or gardens. These experiments provide insights into how plants grow and respond to various factors in realworld conditions.
Final Thoughts
In conclusion, the independent variable in a plant growth experiment is the variable that is manipulated or changed by the researcher to test its impact on plant growth. It is essential in determining the causal relationship between different factors and plant growth, which can inform agricultural practices and plant breeding techniques. Some examples of independent variables include the amount of water, the type of fertilizer, light intensity, and temperature. Researchers can manipulate and control these variables to understand their effects on plant growth.
When conducting plant growth experiments, researchers have various types and options available to them. Comparative experiments, control experiments, factorial experiments, and field experiments are common approaches that allow researchers to investigate different aspects of plant growth. These types of experiments enable researchers to compare different conditions, establish baseline comparisons, analyze the effects of multiple variables, and observe plant growth in realworld environments. By utilizing these different approaches, researchers can gain a comprehensive understanding of plant growth and the factors that influence it.
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Here are several examples of independent and dependent variables in experiments: In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score. You want to know which brand of fertilizer is best for your plants.
There are two key variables in every experiment: the independent variable and the dependent variable. Independent variable: What the scientist changes or what changes on its own. Dependent variable: What is being studied/measured. The independent variable (sometimes known as the manipulated variable) is the variable whose change isn't affected ...
This hypothesis, called the null hypothesis, is evaluated with an experiment to test crop yield response against a range of N rates in a field likely to produce a large response to the addition of N fertilizer. ... In statistical terms, fertilizer rate research employs various levels of a quantitative variable, the amount of fertilizer. If the ...
The variable that affects the dependent variable is called the independent variable. In the plant experiment, the independent variable could be fertilizer—some plants will get fertilizer, others will not. The scientists change the amount of the independent variable (the fertilizer) to observe the effects on the dependent variable (plant growth).
to know that the independent variable is what caused the change, all other variables must not be manipulated. Those variables are called control variables, and they remain constant and unchanged between the two groups in the experiment. In this experiment, the addition of fertilizer is the independent variable manipulated by the scientist.
For example, in a plant growth study, the independent variables might be soil moisture (continuous) and type of fertilizer (categorical). Statistical models will estimate effect sizes for the independent variables. ... They also don't set the values of the predictors. Some independent variables are the experiment's focus, while others help ...
The independent variable is the amount of fertilizer you put on the crop. It is the variable that you, as the tester, vary yourself. ... This makes the temperature of the water a dependent variable. As an experiment you might start with a pot of water at room temperature and heat it up on the stove. You could set the dial to low, medium or high ...
The independent variable, fertilizer treatment, can also be defined in numerous ways that will help specify experimental questions. A single fertilizer treatment with different levels can be tested, or multiple fertilizers compared. ... The simplest experiment has one response variable, one negative control, and one treatment. If experimental ...
In order to make sure that only one factor is being changed in an experiment, the independent variables are then divided into two groups. One group, called the control group, is exposed to all ... experiment PLUS the one variable being tested by the experiment. In the fertilizer example, the investigator must be sure that the peanuts don't grow ...
The independent variable, fertilizer treatment, can also be defined in numerous ways that will help specify experimental questions. A single fertilizer treatment with different levels can be tested, or multiple fertilizers compared. ... The simplest experiment has one response variable, one negative control, and one treatment. If experimental ...
The " variables " are any factor, trait, or condition that can be changed in the experiment and that can have an effect on the outcome of the experiment. An experiment can have three kinds of variables: i ndependent, dependent, and controlled. The independent variable is one single factor that is changed by the scientist followed by ...
The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable. Example: Independent and dependent variables. You design a study to test whether changes in room temperature have an effect on math test scores.
In this case, the independent variable is the type of fertilizer used on your plants while the dependent variable is the rate of growth among your plants. If there is a significant difference in growth between the two groups, then your study provides support to suggest that the fertilizer causes higher rates of plant growth.
The variable that affects the dependent variable is called the independent variable. In the plant experiment, the independent variable could be fertilizer—some plants will get fertilizer, others will not. The scientists change the amount of the independent variable (the fertilizer) to observe the effects on the dependent variable (plant growth).
Figure 1. Adding fertilizers containing nitrogen to the soil can help plants grow well. In this experiment, you will compare plants grown without nitrogen fertilizer to plants grown with nitrogen fertilizer. You will observe the effects of nitrogen on the health of the plants by measuring the increase in biomass (the total mass, or weight, of ...
Similarly, a dependent variable may be referred to as the explained variable, response variable, predicted variable, and so on. As an example, in an experiment that measures the growth of a group of plants that are given varying amounts of fertilizer, the independent variable is the amount of fertilizer administered, and the dependent variable ...
In an experiment, there are two types of variables: The independent variable: The variable that an experimenter changes or controls so that they can observe the effects on the dependent variable. The dependent variable: The variable being measured in an experiment that is "dependent" on the independent variable. In an experiment, a researcher wants to understand how changes in an ...
In the context of a plant growth experiment, the independent variable refers to the factor that is being altered to examine its impact on the growth of the plants. This variable can be any aspect that the researcher wants to investigate, such as the type of fertilizer used, the amount of water provided, the intensity and duration of light ...
In an experiment, independent variables are the quantities you change in order to change other quantities. For instance, if you were doing an experiment in which you want to find out how the number of hours of sunlight exposure affects plant growth, you might have two variables: number of hours of sunlight given to the plant per day, and the ...
Independent Variable: The type of exercise routine is the independent variable. You are trying out different exercise routines each week to see which one makes you feel the most energetic. Scenario Three: Plant Fertilizer. Independent Variable: The type of fertilizer is the independent variable. You are using different types of fertilizer to ...
The scientists change the amount of the independent variable (the fertilizer) to observe the effects on the dependent variable (plant growth). An experiment needs to be run simultaneously in which no fertilizer is given to the plant. This would be known as a control experiment . The plants that do not receive the fertilizer are the control group.
Study with Quizlet and memorize flashcards containing terms like 1, What variable in this experiment? a. the amount of fertilizer received. b. the temperature. c. the hours of light received. d. the amount of growth exhibited by the plants. e. a and c only., 2. What is the independent variable in this experiment? a. the amount of fertilizer received. b. the temperature. c. the hours of light ...
The independent variable in Sherri's experiment is the type of fertilizer used. The dependent variable is the daily growth of the plants. The controlled variables include the type of plant, the amount of sunlight received, and the amount of water given daily. Explanation: In this experiment, the independent variable is the fertilizer given to ...