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1.5 – Variables

Now let’s get into some of the specific terminologies that are used in scientific research. As we discussed earlier, most research explores the relationships between concepts. In other words, as one concept changes (e.g., getting therapy or not) does another concept change (e.g., does depression improve)? When we are looking at concepts that can change or differ among people, we call them variables. Variables are measures of a concept where people vary in terms of that concept. They might have it or not, or they might have more or less of it. Take height, for example. Some people are taller. Some people are shorter. Thus, height is a variable.

In our psychotherapy example, psychotherapy was a variable (some of the participants received it, others did not), as was depression (some participants were more depressed and some were less depressed). That research simply looked at the relationship between those two variables.

A constant, on the other hand, is a concept in which all the participants do not vary. For example, let’s say we wanted to see if math anxiety predicts poor math test performance, but only for females. In this scenario, gender would be a constant because all of the participants in the study are female.

Usually, concepts are held constant by the researcher as a way to make sure that a difference in that particular concept does not have an effect on the variables of interest. In the above example, by holding gender constant the researcher can make sure that gender is not getting in the way of seeing the relationship between math anxiety and test performance. In other words, constants are used by researchers as a way to keep some concepts out of the way so that they can focus on the relationships between the variables in which they are most interested.

Independent and Dependent Variables

When it comes to variables, we can also get more specific in our terminology regarding different types of variables. A dependent variable (DV) is a variable that is measured in a research study. In our psychotherapy example, we measured our participants’ depression levels, thus depression would be a dependent variable in that study. The word “dependent” is used because the resulting measurements were dependent on the participants. In other words, a particular participant’s measurement depends on how depressed they are and how they responded to the way the measurement was performed (e.g., self-report questionnaire, interview, physical measurement, etc.).

An independent variable (IV), on the other hand, is a variable that is manipulated by the researchers. In our psychotherapy example, the researchers manipulated which participants received therapy and which ones did not, thus psychotherapy would be an independent variable in that study. In this case, the word “independent” is used because the group in which a participant was placed was independent of (or not connected to) the participants. In other words, the participants didn’t get to choose whether they received psychotherapy or not.

Being able to identify independent and dependent variables is an important skill when examining research. Now that we have the formal definitions, let’s discuss some other helpful hints that can help in the identification. First of all, independent and dependent variables are found in experiments where we are looking at causal relationships. Specifically, we are looking to see whether the independent variable causes the dependent variable to change. It can be helpful to visualize this with the following:

IV → DV

In an experiment, we want to see if the independent variable has an impact on (thus, the arrow) the dependent variable. If, for example, a researcher is exploring which pain reliever reduces headache pain better, you can see that they are looking at how different pain relievers affect pain.

Type of Pain Reliever → Pain

Thus, the type of pain reliever is the independent variable and pain is the dependent variable.

Another way to distinguish between independent and dependent variables is to think of the independent variable as a grouping variable, while the dependent variable is a measured variable. Because a scientific experiment requires that the researcher manipulates the independent variable, that results in the researcher typically putting participants into different conditions (e.g., getting the drug or not, or getting drug A or drug B), in other words, into different groups. The dependent variable, on the other hand, is simply what is then measured in the study. Thus, in our pain reliever study, we might see that participants either were given ibuprofen (Advil) or Acetaminophen (Tylenol). and then their pain level was measured. Thus, there are two conditions, or groups, and thus the type of pain reliever must be the independent variable. And because we measure their pain level, pain must be the dependent variable.

We can further differentiate independent variables using some other terminology. First of all, when recognizing that the independent variable creates conditions or groups, it is often helpful to know more about those conditions. The levels of the independent variable refer to the different conditions created in the research study. In our pain reliever study, we have two conditions, so we can say that the independent variable, pain reliever, has two levels: ibuprofen and acetaminophen. You will see later that the number of levels of the independent variable is an important factor in determining which specific statistic we will use.

We can also explore the levels of our dependent variables. In this case, the levels are all the possible outcomes of our measurement. For example, let’s say our dependent variable is the score on a statistics exam, and that exam has 100 multiple-choice items, each worth one point. Thus, the levels for that dependent variable would be all the scores between 0 and 100 in intervals of 1, which would mean there are 101 levels. Because there can often be an infinite number of levels for some dependent variables, we rarely will need to explore the levels of dependent variables.

Quasi-Independent Variables

Remember from the previous section that it is not always possible to do a true experiment because we sometimes cannot easily manipulate the independent variable. The alternative, then, is to run a quasi-experiment where you record the conditions in which participants were already naturally divided (e.g., earthquake or not). When you don’t randomly assign participants to the research conditions, that variable is no longer an independent variable but is instead technically called a quasi-independent variable.

This distinction does not typically affect the statistical procedure we will choose to use. However, it will definitely affect our interpretation of the statistical results because we cannot determine any causal effect.

Operational Definitions

As we stated before, variables vary. If people vary in the concept in which we are interested, we need to how exactly they differ, and often we want to express these differences quantitatively, meaning with numbers. Additionally, there are often multiple options available to a researcher when they are deciding how to measure a particular variable. For example, let’s say we want to measure “memory.” There are hundreds, if not hundreds of thousands of ways to go about measuring memory. We could simply read off a list of numbers and ask people to repeat them back, increasing the number of digits each trial. Or we could hand people a list of 40 words and give them 5 minutes to memorize as many as they can, and then ask them to say or write all the words they remember.

The question of how a variable is measured is called the operational definition of the variable. It describes how a variable was “operationalized,” meaning how it was measured or expressed quantitatively.

If we are working with an independent variable, the operational definition simply describes or defines how the variable was manipulated, in other words, how the groups or conditions were created. In our psychotherapy study, the operational definition of the independent variable, psychotherapy, might be a condition where the participants received 10 weeks of psychotherapy and a condition where the participants received no psychotherapy.

If we are working with a dependent variable, the operational definition describes or defines how the variable was measured. In our psychotherapy study, the dependent variable was depression level. Well, how did we measure depression? There are many ways researchers can do this. For instance, they might use a self-report depression scale, or they might use a formal psychiatric diagnosis. There are many options. Thus, it becomes important for research to specify their operational definitions.

This transparency regarding how researchers operationally define their variables allows people reading the research to decide for themselves if they think the way the variables were operationally defined well enough. For example, suppose in our psychotherapy study they operationally defined depression by having participants answer the yes or no question: are you depressed? You might decide that this is a poor way to measure depression, and thus you can then be more skeptical about the results of that study.

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Introduction to Statistics and Statistical Thinking Copyright © 2022 by Eric Haas is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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