Is there a p value correction for dealing with multiple hypothesis testing when I want to know how many tests satisfy p > alpha (ie, how many tests fail to come up with a 'significant' result) instead of p < alpha? For example, for a Bonferroni correction, alpha/(number of tests) makes sense to me for a very conservative threshold, but this has always been explained to me in the context of p < alpha, no the opposite. Would it be valid to multiply p by the number of tests?
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A partial answer to:
Would it be valid to multiply p by the number of tests?
This would result in the Bonferroni adjustment, since this $p$-value adjustment would be equivalent to your stated $\alpha$-level adjustment of $\alpha$ divided by number of tests.
If you just mistyped and you asked about adjusting the $\alpha$-level to $\alpha$ times number of tests - no, since this could reach 1 for large enough number of tests.
