Let's say I have an experiment with a 2x2 repeated-measures design. Let's call the four cells A1B1, A1B2, A2B1, A2B2, for the factors A and B, each with two conditions, labeled 1 and 2.
I want to compute the power needed for a main effect of A, and for an interaction, reflecting a moderation of the effect of A in different levels of B.
I plan to analyze the data using a repeated measures ANOVA.
My question is about the implications of using a power analysis for t-test in order to determine the sample size. (I am putting aside the question of how to determine the desired effect size; let's say I know it is d=0.2).
To be specific, for the main effect of factor A, I will run a power analysis for a dependent-samples t-test that will compare the average of A1 and the average of A2. For the interaction, I will run a power analysis for a dependent-samples t-test that will compare the average of A2B1-A1B1 and the average of A2B2-A1B2.
Is there any risk of underestimation of the required sample-size?
The more general question is about this method for other designs as well. Any effect in an ANOVA can be tested in a t-test. That is not recommended, of course, but for the power-analysis, is there any risk of underestimating the required sample size in computing the power for that t-test?