The other way to do Bonferroni: adjust the p-value

Question

You ran 15 hypothesis tests. One of them returned a raw p-value of 0.004. Rather than shrink your cutoff, you want to report a single "corrected" p-value you can compare against the usual 0.05.

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

Accepted Answer

Two equivalent views of Bonferroni. You can either shrink the cutoff (compare the raw p to \alpha/m) or inflate the p-value (compare m 	imes p to the ordinary \alpha). They give identical decisions, the second is handy because you can hand someone one number and let them use the familiar 0.05 line. Adjust the p-value. The Bonferroni-adjusted p-value is the raw p-value multiplied by the number of tests: p{	ext{adj}} = m 	imes p = 15 	imes 0.004 = 0.06. Decide. Compare 0.06 to the usual 0.05. Since 0.06 0.05, the result is not significant after correction. Check the two views agree. The shr…

The other way to do Bonferroni: adjust the p-value

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