What this answers

This calculator answers "given several p-values from tests I ran together, how should each one be adjusted so my overall false-positive rate across the whole family stays controlled?" Testing many hypotheses without any correction inflates the chance that at least one comes back significant purely by chance.

How it is calculated

Each p-value is multiplied by the family size (the total number of tests being considered together), capped at 1. Equivalently, you can compare each raw p-value against an adjusted alpha threshold of alpha divided by the family size. Both views describe the same correction; this calculator shows both. Bonferroni does not decide which tests belong in the family; you must declare that yourself, and it can differ from the number of p-values you happen to enter here if you know the true family is larger.

Worked example

For raw p-values of .01 and .03 with a family size of 2, the adjusted p-values are .02 and .06. At the conventional .05 threshold, the first comparison remains significant after correction while the second, originally below .05, no longer is, exactly the kind of result an uncorrected analysis would have missed.

Assumption audit

Calculated from your data: each adjusted p-value and the corresponding adjusted alpha threshold, given your declared family size.

Evidence to review: whether your declared family size actually matches every comparison a reader would consider part of the same analysis; under-declaring the family size (for example, by only counting the tests you eventually report) defeats the purpose of the correction.

You must verify: which specific tests genuinely belong in the same family; Bonferroni corrects for the number you tell it, not the number you should have told it.

What this result does not mean

Surviving Bonferroni correction means a result remains significant even under this conservative adjustment, a fairly strong claim; failing to survive it does not mean there is no real effect, since Bonferroni is deliberately conservative and can miss real, smaller effects, especially as the family size grows large.

Limitations

Bonferroni is the simplest and most conservative common correction; for many post-hoc comparisons following an omnibus test, Holm's step-down method (used automatically by the Dunn Post-Hoc Test on this site) offers more power while still controlling the same family-wise error rate.