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I am comparing two groups (young vs. old adults) for differences in 5 brain regions (size) with independent t-tests. I also compare performance on three different aspects of a task with independent t-tests and then correlate brain sizes and behavioral performance . I adjusted my p-values (Bonferroni-method) for the correlations (for the five brain regions), but I am not sure, how exactly/if I have to adjust the p-values for each independent t-test between the age groups. I have a priori hypotheses about all comparisons. Any help would be highly appreciated!

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  • $\begingroup$ Welcome to Cross Validated, Isabel. Before asking how to correct for multiple comparisons, you might consider whether you should correct. See here for some discussion: stats.stackexchange.com/questions/3200/… $\endgroup$ – Michael Lew Nov 21 '18 at 20:08
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If your study is preliminary, or if it is about characterisation rather than testing hypotheses then you probably should not `correct' for multiple comparisons. The raw P-values give you the strength of evidence against the individual null hypotheses and are should be presented alongside a more detailed presentation of the data.

If you decide that you should `correct' then you will have to decide whether to treat all of your comparisons as part of the family or whether your experiments consist of a couple of families. I would suppose that the brain size tests are one family and the behavioural tests are another.

Finally, you might consider a slightly less power-wasting form of multiplicity correction like one of the step-down procedures (search for Šidák and step-down).

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