Analysis of Variance

This chapter introduces students to the One-Way Between-Groups Analysis of Variance (ANOVA). We begin with a brief discussion of the rationale for the ANOVA, describing how it allows us to compare many more levels of an independent variable than we could manage with the t-test. We explain that the One-Way Between-Groups ANOVA specifically utilizes one independent variable and one dependent variable measured on the interval or ratio scale and that each participant is measured only once. We use two simple examples to teach students how to complete calculations of the ANOVA by hand. In the first example, we want to know if research participants prefer the scent of one of two perfumes (the two treatment groups) or water (the control group). In the second example, we compare the effects of eating a simple or well-balanced breakfast (the two treatment groups) to eating no breakfast at all (the control group) on scores on a quiz taken later in the morning. The notation specific to the ANOVA is discussed and, for each example, a data table is organized to present group means, sums of scores, and sums of squared scores in order to prepare students for the ANOVA calculations; in this way, students begin the calculations with the summary data they need to plug into the equations. In a step-by-step manner, we walk students through using equations to calculate the Sums of Squares, degrees of freedom, Mean Square Variances, and the F-ratio. Statistics are organized into the ANOVA Source Table, and hypothesis testing for the F-ratio is interpreted using the statistical table of critical values for the F-distribution. A discussion of effect size, using eta-squared, follows. This chapter also discusses the limitation of the ANOVA, in that a significant result does not tell us which mean(s) differs from which other(s). Thus, we guide students through the calculations and interpretation of Tukey’s Honestly Significant Difference (HSD). Results for both examples are presented in APA (seventh edition) formatting. Sidebar notes explain why we cannot simply run multiple t-tests instead of the ANOVA and warn students of common mistakes and pitfalls when calculating the ANOVA. A biography box presents information about Ronald Fisher. Concluding the chapter, a brief summary reminds students of important concepts. Step-by-step illustrated instructions show students how to use Excel’s Data Analysis Toolpak to calculate the ANOVA. Critical thinking questions and practice problems are provided.