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412 PART V: Analyzing and Reporting Researchwere first introduced. Using this method will help determine whether thereis an interaction effect. Examining the differences between the two means fora 1 and a 2 at each level of B (b 1 , b 2 , b 3 ) will show that the three differences (8.4,3.2, 1.8) are different. This suggests that an interaction effect is present. As youlearned in Chapter 8, graphing the means also will help you see the nature ofthis interaction effect. Let us assume that an omnibus F-test has confirmed thatthe interaction effect was statistically significant (p .05).Once we have confirmed that there is an interaction of two independentvariables, we must locate more precisely the source of that interaction effect.There are statistical tests specifically designed for tracing the source of asignificant interaction effect. Theses tests are called simple main effects andcomparisons of two means (see Keppel, 1991) and were discussed briefly inChapter 8. Comparisons between two means were also described earlier inthis chapter.Recall that a simple main effect is the effect of one independent variable at onelevel of a second independent variable. In fact, one definition of an interactioneffect is that the simple main effects across levels are different. In a 2 3 designthere are actually five simple main effects. Three of the simple main effects arerepresented by the effect of Variable A at each level of Variable B. The other twosimple main effects are represented by the effect of Variable B at each level ofVariable A. Which set of simple main effects are chosen for analysis will dependon the rationale behind the experiment. That is, it may be more important forinterpreting the results to highlight one set of simple main effects more thananother. Of course, finding that simple main effects are different for levels ofeither variable indicates an interaction effect.How do we compute a simple main effect? Statistical software packagesdo not always permit simple main effects analyses to be computed and, whenthey do, can vary in the specific computational procedures that are followed.There are relatively simple ways to do these analyses with a calculator (e.g.,Zechmeister & Posavac, 2003). However, let us suggest the following procedurethat is easily done using an ANOVA software package.Consider our example above. Suppose we wish to analyze the simple maineffect for the first level of variable A, that is, for a 1 . There are three “groups”(a 1 b 1 , a 1 b 2 , a 1 b 3 ) in this analysis. One approach is to perform a simple (one-way)independent groups ANOVA for these data. In other words, assume that thereare three random groups of participants assigned to three levels of an independentvariable. Carry out this analysis and identify in the ANOVA SummaryTable the mean square (MS) between groups (i.e., the MS for the effect of yourvariable). It is the sum of squares between groups divided by its df, which is thenumber of groups minus 1, or, in this case, 3 1, and df 2. To obtain an F-ratioyou want to divide the MS between groups from this analysis by the MSerror(within groups) based on the overall F-test that you originally performed whenexamining effects in the 2 3 complex design. In our example, with 30 participantsthe df for the MSerror in the 2 3 design will be 24, so the critical F is thatassociated with 2 and 24 degrees of freedom.Two of the simple main effects in our hypothetical experiment involve threemeans (i.e., levels a 1 and a 2 across three levels of B). If a statistical analysis reveals