I would like to perform an a priori power analysis to calculate required sample size for data to be analyzed using one way ANOVA and Tukey HSD post hoc test. (I want to determine pair-wise which groups are different from each other)
desired significance level (alpha): 0.05 desired power: 0.9 cohens effect size: 0.4 nr of groups: 3 or 5
I want to calculate sample size. I have used G*Power but it seems to only provide the power analysis for ANOVA omnibus test but not the post hoc test.
Alternatively, would it be valid (and conservative) to correct alpha a la Bonferroni by dividing 0.05 by the number of the unplanned multiple comparisons? (e.g. 0.05/3 for three groups or 0.05/10 for 5 groups) and use that lower alpha for G*Power's f-test power analysis?
Or should I count up all pair-wise comparisons and perform a power analysis for a t-test using this Bonferroni adjusted alpha?
Can anyone provide a reference or software or any other guidance on how to proceed?