Why is a two-way mixed factorial ANOVA involving six conditions more powerful than a between-groups ANOVA with involving three conditions? I understand that between-groups analyses are less powerful as subject variance is not removed (Greenwald, 1976). But why is a mixed factorial ANOVA more powerful (i.e., requires lower N to detect significant main effects and interactions) when it still involves between-group comparisons? Grateful for anyone who can shed some light on this for me.
Since you used G*power, I'm wondering if you saw that by adding a repeated measures (within subjects) factor to a one factor between subjects design, thus ending up with two (mixed), you saw that you did not need to increase the number of participants necessary to detect the effects at (say) 80% power?
Power is specific to a single hypothesis test, it is the probability that you will reject the null hypothesis if indeed there is a "real" effect to detect. So going from one factor to two increases the number of hypothesis tests you perform, but does not inflate the Type I error rate (the probability of falsely rejecting the null). The mixed design means you also don't need any more participants than you already have because you can vary the repeated measures factor across different time points in the same sample of participants. Thus, power seems to be increased, but it is really that you get more bang for your buck with the design.