Effect size in contrast analysis I'm running 2-way repeated measures ANOVA (3 and 5 levels) with planned contrasts afterwards. I'm interested in comparing 
1)levels of the first factor among themselves (e.g. A1B with A2B, A2B with A3B)
2)pairwise comparisons (e.g. A1B1 and A2B4)
Question:
Some sources claim that I need to report effect size for each contrast. I wonder if this makes sense since the design is repeated measures. If so, how the contrasts should be calculated? I don't think the standard formula for Cohen's d works in this case since it doesn't take into account the correlation.
 A: Your effect sizes for your pairwise contrasts would be derived from the test that is associated with the effect.  For example, if you are doing a pairwise t-test comparing cells of your design, then your effect sizes would be derived from each of those pairwise t-tests (using whatever error term you select for those pairwise tests).  As a pairwise t-test is computationally equivalent to a one-sample t-test, you should be able to calculate the Cohen's d using the formula $\bar{d}\over{s_{d}}$ (although this is what is commonly considered Cohen's d, I understand that Cohen's formulas actually reflected the use of $\sigma$).
A: If you are doing this using conventional ANOVA, you are making a mistake. This should be done as a mixed-effect repeated measures (MERM) model. The test of sphericity is 30 years out of date. Using mixed-effects models, you define a proper covariance model (which may include the compound symmetry model, but usually does not), and test things properly. These tests are done using PROC MIXED in SAS, also can be done in R or SPSS. Many programs do not do these correctly. If the program warns you about compound symmetry, you are using a bad program. And for those who are warning about compound symmetry and the GG correction, you need to update your methodology. You are out of date. And if you do use MERM, it is easy to specify contrasts. I do this all the time - in SAS. FInally, do not do repeated paired t-tests. Very much the wrong approach. You need to fit the entire design, define contrasts which properly compare between levels, and use the procedure defined error term.
