Adjusted p-value for a borderline raw result

Question

Out of 8 hypothesis tests, your best result had a raw p-value of 0.009. You want to report a single corrected p-value comparable to the familiar 0.05 threshold.

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

Accepted Answer

Multiply by the count. The Bonferroni-adjusted p-value inflates the raw p-value by the number of tests, so it can be judged against the plain 0.05. Adjust. With m = 8 and raw p = 0.009: p{	ext{adj}} = m 	imes p = 8 	imes 0.009 = 0.072. Decide. Since 0.072 0.05, the result is not significant after correction, despite the raw p of 0.009 looking respectable on its own. The takeaway in miniature. A raw p under 0.01 is easy to over-trust. Once you remember it was the pick of eight tries, the honest adjusted value is 0.072, just over the line. This is a classic "looked significant, was not" case…

Adjusted p-value for a borderline raw result

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