Adjusted p-value that still clears the bar

Question

You ran 20 hypothesis tests. One returned a raw p-value of 0.001. You want a single corrected number to compare against the usual 5% line.

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

Accepted Answer

Inflate instead of shrink. Bonferroni can be applied by multiplying the raw p-value by the number of tests, then comparing to the ordinary 0.05. This is equivalent to shrinking the cutoff, but reports one clean number. Adjust. With m = 20 tests and raw p = 0.001: p{	ext{adj}} = m 	imes p = 20 	imes 0.001 = 0.02. Decide. Since 0.02 < 0.05, the result is significant even after correcting for 20 tests. Why it survives. A raw p of 0.001 is strong enough that even a twenty-fold penalty leaves it under 0.05. That is the mark of a genuinely robust finding: it stays significant after you honestly …

Adjusted p-value that still clears the bar

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