The Smallest of Ten p-values
Ten independent hypothesis tests are run, and in fact all ten null hypotheses are true, so each p-value is uniform on [0, 1]. The smallest of the ten p-values is reported. If the reported value is 0.004, what is the probability, under this all-null setting, that the smallest of ten p-values would be at most 0.004? (This is the Sidak-adjusted p-value.) Give your answer rounded to 4 decimal places; 3 decimal places is also accepted.
Related problems & prerequisites
Worth solving first
- Two Hits Among Twenty Nulls 4.0/10
Source: Standard Sidak-correction exercise on selecting the best of several tests. Statement written for AxiomIQ.