Essentials

FACTORIAL ANOVA 167sual method (relative to the grand mean), .07 is the effect of text C, and .38 isthe amount of interaction that results from combining the visual method withtext C (apparently they go together well).As you would imagine, the GLM becomes increasingly complex as factors areadded to an ANOVA. For instance, the GLM for the three-way ANOVA is Y ijkl i j k i j i k j k i j k ε ijkl, where (the Greekletter gamma) represents the third variable. The GLM allows you to mix bothqualitative and quantitative IVs in the same design. Among other uses, the GLMprovides a straightforward way to understand how the effects of a quantitativenuisance variable can be removed from an ANOVA by means of a procedurementioned earlier, known as ANCOVA. One way that ANCOVA can increasethe power of your ANOVA is by reducing the error term. Another powerful wayto reduce your error term involves repeated measures, or, alternatively, the matchingof participants. These procedures will be discussed in the next chapter.Putting It Into Practice1. As in exercise 1 in chapter 5, participants were measured on a 10-point depressionscale after taking one or another of the following drugs for sixmonths: a placebo, a natural herb (St. John’s Wort), a tricyclic antidepressant(Elavil), and an SSRI drug (Prozac). All of the participants in the previous exercisewere men; an equal number of women participants has been added tothis exercise. The mean depression rating for each group is shown in the followingtable.Placebo St. John’s Wort Elavil ProzacMen 9 8 4 3Women 8 2 5 1(a) Given that there are 11 participants in each group and that MS Wequals32, calculate the F ratios to test all three null hypotheses.(b) Calculate and test the simple main effect of drug for each gender.(c) Calculate the interaction contrast for gender by St. John’s Wort/Elavil, andtest for significance. If this were a post hoc contrast, would it be significantby Scheffé’s test?2. The following table is being reprinted from Gist, Rosen, and Schwoerer(1988). Participants in this study were trained on a particular computer skill byone of two methods and were classified into one of two age groups. Meanperformance (along with SD and n) on the computer task is given for each ofthe four subgroups (cells).(continued )