ANOVA: Comparisons of Several Populations

Abstract

In Chapter 11, we demonstrate the use of t-tests for comparing the means of two populations (such as males and females). The analysis of variance (ANOVA) allows us to compare the means of a larger number of populations (i.e., three or more). Through analysis of variance, variability among the group means is compared to the variability within the groups. If between-group variability is substantially greater than within-group variability, the means are declared to be significantly different. The ANOVA allows you to answer questions such as: Is political affiliation (Democrat, Republican, Independent) related to the number of elections in which people vote? Do three different techniques for memorizing words have different impacts on the mean number of words recalled? Is annual movie income from movie sales related to the type of movie (e.g., comedy, drama, horror, action, family)? Is heart rate after a step-workout affected by the height of the step (low or high) and the frequency of stepping (slow, medium, fast)? In this chapter, we will use the One-Way ANOVA procedure in SPSS. We will also discuss techniques for obtaining follow-up tests to determine which group means differ from which others, and effect sizes to determine the magnitude of the differences between specific groups. We will also explore the Analysis of Variance of Ranks, which is appropriate when the assumptions required for performing ANOVA are violated. Finally, we will use the General Linear