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CHAPTER 12: Data Analysis and Interpretation: Part II. Tests of Statistical Significance and the Analysis Story 411computer- assisted analysis of a factorial design that involves F-tests for themain effect of A, the main effect of B, and the interaction effect, A B. The twofactoranalysis for independent groups is applicable to experiments in whichboth independent variables are manipulated using a random groups design,in which both independent variables represent the natural groups design, or inwhich one independent variable represents the natural groups design and theother represents the random groups design. As we noted in Chapter 8, the analysisof a complex design proceeds somewhat differently depending on whetherthe omnibus F-test does or does not reveal an interaction effect. We first considerthe analysis plan when an interaction effect is detected.Analysis of a Complex Designwith an Interaction Effect• If the omnibus analysis of variance reveals a statistically significant interactioneffect, the source of the interaction effect is identified using simplemain effects analyses and comparisons of two means.• A simple main effect is the effect of one independent variable at one level ofa second independent variable.• If an independent variable has three or more levels, comparisons of twomeans can be used to examine the source of a simple main effect bycomparing means two at a time.• Confidence intervals may be drawn around group means to provide informationregarding the precision of estimation of population means.Consider a hypothetical complex design involving two independent variables(A B), each involving independent groups (random groups or naturalgroups). Variable A has two levels and Variable B has three levels. Thus, thedesign is a 2 3 independent groups design. The details of the experimentneed not concern us, although let us assume there are five participants in eachgroup (n 5; N 30). Table 12.5 shows mean performance for the six groupsin this example. By now we trust that you know first to examine the summarystatistics to see what trends are present in the data. How would you describethe results seen in Table 12.5? One way would be to state that there was verylittle difference among means across three levels of B for the first level of A,that is, for level a 1 . On the other hand, means changed quite a bit across thesame three levels of B for level a 2 . Yet another way to describe these results is touse the subtraction method we discussed in Chapter 8 when complex designsTABLE 12.5MEAN PERFORMANCE OF GROUPS IN HYPOTHETICAL 2 3 DESIGNVariable Bb 1 b 2 b 3Variable Aa 1 19.0 19.0 20.0a 2 10.6 15.8 18.2