Introduction: Thinking about the Number and Scale of Your Variables

Researchers are often confused by the task of choosing the correct statistical procedure for analyzing a given dataset. There are so many procedures from which to choose that it is easy to become frustrated, not knowing where to begin. This appendix addresses this problem by providing a relatively simple system for classifying statistics. It provides a structured approach that should make it easier to find the appropriate statistical procedure for a wide variety of circumstances.

In a sense, most statistical procedures involve examining the relationship between two variables (or two sets of variables). In a given study, the outcome variable that you are interested in is called either a criterion variable (in nonexperimental research) or a dependent variable (in experimental research). In nonexperimental research, you study the relationship between the criterion variable and some predictor variable with values that are used to predict scores on the criterion (in experimental research, a manipulated independent variable is the counterpart to this predictor variable). In general, nonexperimental research involves examining the relationship between a criterion variable and a predictor variable whereas experimental research examines the relationship between a dependent variable and an independent variable or variables. To simplify matters, this appendix blurs the distinction between nonexperimental versus experimental research, and uses “criterion variable” to represent criterion variables as well as dependent variables, and uses “predictor variable” to represent predictor variables as well as independent variables.

Thinking about Your Criterion Variables

Two primary factors that determine the selection of an appropriate statistical procedure are the number and the scale of the criterion variables. The number merely refers to how many criterion variables appear in the dataset, while the scale refers to the level of measurement used in assessing these criterion variables (i.e., nominal, ordinal, ratio, or interval).

For example, assume that you want to conduct a study to learn about variables that predict success in college. In your study, you might choose to use just one criterion variable as an index of college success such as grade point average (GPA). Alternatively, you might choose to use several criterion variables so that you will have multiple indices of success such as college GPA, college class rank, and whether or not participants were inducted into some college honorary society (yes versus no). Here, you can see that the number of criterion variables varies. In the first case, there is only one criterion variable; in the second, there are three.

Notice, however, that the scale used to assess college success also varies. The criterion variable college GPA is assessed on an interval scale, college class rank is assessed on an ordinal scale, and induction into an honorary society is assessed on a nominal scale. The number of criterion variables used in the analysis, as well as the scale used to measure those variables, helps to determine which statistic you can use to analyze your data.

Thinking about Your Predictor Variables

However, you still do not have enough information to choose the appropriate statistic. Two additional factors that determine choice of the correct statistic are the number and scale of the predictor variables. Again, consider the college success study in which you are interested in learning about variables that predict college success. Assume that you have decided to use just one criterion variable as a measure of success: college GPA. You might choose to design a study that also includes just one predictor variable: high school GPA. Alternatively, you can design a study that includes multiple predictor variables such as high school GPA, scores on the SAT, high school rank, and whether the student received a scholarship (yes versus no).

In the previous paragraph, notice that the number of predictor variables that might be included in a study varies. The first study included just one predictor, while the second included multiple predictors. Note that the scale used to assess these predictors also varies. Predictors were assessed on an interval scale (high school GPA, SAT scores), an ordinal scale (high school rank), and a nominal scale (whether the student received a scholarship). The number of predictor variables included in your study as well as their scale also help determine the appropriate statistic.

Putting It Together

The preceding discussion has provided context for the following recommendation. When choosing the appropriate statistic for an analysis, always consider the following:

• the number and scale of the criterion variables, in conjunction with;

• the number and scale of the predictor variables.

For example, imagine that in your study, you used only one measure of college success (GPA) and one predictor variable (SAT scores). Since you have a single criterion variable assessed on an interval scale and a single predictor variable also on an interval scale, you know that the appropriate statistic is the Pearson correlation coefficient (assuming that a few additional assumptions are met). But what if you modify your study so that it still contained only one criterion variable but now contains two predictor variables, both assessed on an interval scale (e.g., SAT scores and high school GPA)? In the latter case, it would be more appropriate to analyze your data using multiple regression.

This is the approach recommended in this appendix. To select the right statistic, consider the number and nature of both your criterion and predictor variables. To facilitate this decision-making process, this appendix includes three tables: one that lists statistics for studies that involve a single criterion variable and a single predictor; one for studies that involve a single criterion variable and multiple predictors; and a final table for studies with multiple criterion variables.

A few words of caution are warranted before presenting the tables. First, these tables were not designed to present an exhaustive list of statistical procedures. They focus only on the tests that are the most commonly used in the social sciences. A good number of statistical procedures that did not fit neatly into this format (such as principal component analysis) do not appear. Second, these tables do not necessarily provide all of the information that you need to make the final selection of a statistical procedure. Many statistical procedures require that a number of assumptions be met concerning the data for the procedure to be appropriate, and these assumptions are often too numerous to include in a short appendix such as this. The purpose of this appendix is to help you locate the statistic that may be correct for your situation given the nature of the variables. It is then up to you to learn more about the assumptions for that statistic to determine whether your data satisfy those assumptions.