[R-sig-ME] Is multiple-hypothesis-testing correction needed when the goal is decision making?

[Pardis Miri]

Dear forum,

Based on frequentist approach.
Suppose we have an IV of body site with two levels a and b. We have three DVs dv1, dv2, and dv3.  For example, how well the participant attends to the vibrations, how well the participant differentiate the vibrations, and how well the participant synchronizes their breathing with the vibrations.
We have three hypotheses: a > b for dv1, dv2, and dv3. We run a mixed model for each DV. Each results in p-values p1, p2, and p3. We know that if we want to say that all three hypotheses are true, we multiply each p-value by 3 (eg, 3*p1 ,3*p2, and 3*p3) and test if each is less than 0.05.

However, I am instead looking for some evidence - a recommendation - that site a is better than site b. In this case, can we simply say yes if at least one of the p-values is < 0.05? That is, if p1 < 0.05 but p2 and p3 are both > 0.05, we can conclude that the dv1 hypothesis shows evidence, but the two other hypotheses are inconclusive.

Thank you all!
P


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