For X to be considered valid, X needs to pass all K statistical tests, at p < 0.01 each. If X fails any statistical test, the null hypothesis is retained.
K however changes for different X.
In some cases, X needs to pass 10 statistical tests.
In other cases, X needs to pass 100 statistical tests.
Adjusting for FWER, if K = 10, the adjusted alpha is $10^{-2}$. If K = 100, adjusted alpha = $10^{-3}$.
I would like to have a constant FWER across different X.
Is there any way to correct p for multiple "AND" comparisons? It's been extremely difficult researching this topic since almost all online content is about correcting for Alpha risk inflation (whereas here Alpha is deflated).
The obvious solution would be doing a "reverse Bonferroni" correction, and multiply p by the number of comparisons. i.e., to have a FWER of 0.01, I would multiply the original Alpha (= 0.01) by the number of comparisons.
For K = 10 comparisons, the adjusted significance threshold would be < 0.1. Except for K = 100 comparisons, the adjusted threshold would be 1... Something's not right.
Are there papers that discuss of Alpha risk correction where significance is defined as passing all K tests?
Any help would be much appreciated.