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410 PART V: Analyzing and Reporting ResearchFIGURE 12.2Means and 95% confidence intervals for the time-perception experiment.Time-Perception Experiment5040Mean Judgments302010012 24 36 48Time Intervals (seconds)where t crit is the value of t with the degrees of freedom associated with theMS error (residual). The interpretation of confidence intervals in the repeatedmeasures design is the same as that of the independent groups design (seeChapter 11).Effect Size Measures As we mentioned previously, it is a good idea to includemeasures of effect size for your analyses. A typical measure of effect size fora repeated measures design is the strength of association measure called etasquared ( 2 ). It may be calculated by dividing the sum of squares for the withinsubjectseffect by the combined sums of squares for the within-subjects effectand residual or error. For our sample study,SS effect _____________eta squared 2 SS effect SS _____________ 2515.6error 2515.6 646.9 .795This indicates the proportion of variance accounted for by the independentvariable. In some cases, the omnibus analysis of variance would be followedby comparisons of two means as we saw in the independent groups design.TWO-FACTOR ANALYSIS OF VARIANCE FOR INDEPENDENTGROUPS DESIGNSThe two-factor analysis of variance for independent groups designs is used forthe analysis of experiments in which each of two independent variables wasmanipulated at two or more levels. The logic of complex designs with two independentvariables and the conceptual basis for the analysis of these experimentsare described in Chapter 8. In Chapter 8 you also learned to describeboth main effects and interaction effects. We will focus in this chapter on the