Background: As I understand, family-wise error refers to the inflation of Type I error when performing multiple hypothesis tests. For example, if I were to perform multiple post-hoc comparisons following an omnibus ANOVA test, then the collection of post-hoc comparisons would be the "family". As the number of tests increases, the risk of Type I error also increases. Hence, family-wise error corrections (like Bonferroni) adjust the alpha criterion in order to account for this Type I error inflation. For example, if I were to perform 6 tests, then I might divide the normative 0.05 alpha by 6 to obtain an adjusted alpha criterion of 0.008, and use this adjusted alpha to determine significance.
Question: Does the family-wise error logic also apply to effect size calculations? If so, are there any common correction procedures like Bonferroni that can be used to adjust effect sizes like eta-squared or Cohen's D? If not, why not?