A tiny raw p that survives 50 tests

Question

You ran 50 hypothesis tests. One returned a raw p-value of 0.0008. You want a single corrected number to compare to the usual 5% line.

What is the Bonferroni-adjusted p-value, and is it significant at the 5% level?

Accepted Answer

Inflate the p-value. Bonferroni's adjusted p-value multiplies the raw p-value by the number of tests, letting you use the familiar 0.05 cutoff. Adjust. With m = 50 and raw p = 0.0008: p{	ext{adj}} = m 	imes p = 50 	imes 0.0008 = 0.04. Decide. Since 0.04 < 0.05, the result is significant even after correcting for 50 tests. Why it holds up. To survive a fifty-fold penalty, a raw p-value has to be tiny, and 0.0008 is. A finding that clears Bonferroni against 50 tests is unusually credible, exactly the kind of result worth carrying forward to validation. Takeaway. The Bonferroni-adjusted p-val…

A tiny raw p that survives 50 tests

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