Tests on Location: Analysis of Variance and Other Selected Procedures
In Chapter 14 we described several different ways to compare two groups with regard to central tendency, or location. The differences among the procedures related to issues of sample size, conformity to assumptions, and independent/dependent samples. In practice, studies often involve more than two groups, making the use of two-group procedures awkward, at best. In this chapter we will present several extensions of the two-group procedures. More specifically, we will describe the analysis-of-variance (ANOVA), the Kruskal-Wallis test, and randomization tests as each of them may be applied to the k-group situation. We want to remind you that group designs, such as the two-group situation addressed with the t-test and the k-group situation addressed with ANOVA, are really special cases of the more general matter of looking at the relationship between an independent variable and a dependent variable. Just because we employ statistical techniques such as t-and F-tests, we cannot necessarily draw stronger inferences about the possible causal relationship between the two variables. The major difference between group statistics (t-test, ANOVA) and correlational statistics (Pearson’s r, regression) is related to the difference in which the variables are scaled (measured) in different situations. The “group” statistics are merely simplified computational routines to deal with the relationship between a numeric dependent variable and a categorical independent variable. In future statistics courses you will learn about the general linear model as an approach that subsumes many statistical procedures. Keeping this distinction between “design” and “statistical procedure” in mind, let us turn our attention to the k-group situation. For example, imagine that we want to compare White, African American, and Hispanic children with regard to their scores on the General Knowledge measure at the beginning of kindergarten. After introducing the conceptual basis and notation of ANOVA, we will complete an example that will show you how to make such a comparison.