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.
Best Answer
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 $\sigma$).