Bonferroni Correction Calculator
This Bonferroni correction calculator adjusts your significance level for the problem of multiple comparisons, the trap where running many tests on the same data makes a false positive almost inevitable if you keep judging each one at the usual 5% threshold. Every test you run carries its own chance of a chance finding, and those chances add up, so the more comparisons you make the more likely you are to call something significant when it is not. The Bonferroni method is the simplest fix: it divides your chosen family-wise significance level by the number of comparisons to give a stricter per-test threshold, so a result must clear a higher bar before you trust it. Enter your family-wise alpha, the number of comparisons you are making, and optionally a single p-value you want to check, and the calculator returns the corrected threshold, the adjusted p-value, and a plain reading of whether that result survives the correction. Adjusting a p-value works the other way: it multiplies the raw value by the number of comparisons, capped at 1, so you can compare it against your original alpha. Researchers, students and analysts use it whenever they test several hypotheses at once, from a batch of survey questions to a panel of laboratory measures. Bonferroni is deliberately conservative, so with a large number of comparisons consider Holm or Benjamini-Hochberg for more power.
With 10 comparisons the Bonferroni threshold is 0.005, so a raw p-value of 0.008 is not significant after correction (its adjusted p-value is 0.08 against a family-wise 0.05).
Corrected threshold is alpha divided by the number of comparisons; the adjusted p-value is the raw p-value times the number of comparisons, capped at 1. Bonferroni controls the family-wise error rate and is conservative.
How it works
When you run several independent tests, the chance that at least one throws up a false positive grows with the number of tests. The Bonferroni correction keeps the overall, or family-wise, error rate at your chosen alpha by sharing it equally across the comparisons: each test is judged against alpha divided by the number of comparisons. You can apply the correction from either direction. Tighten the threshold by dividing alpha by the number of comparisons and compare each raw p-value to that, or adjust the p-values by multiplying each one by the number of comparisons (capped at 1) and compare them to the original alpha. Both routes give the same significant-or-not verdict.
Worked example
Say you test 10 outcomes and want to hold the overall false-positive rate to 0.05. The Bonferroni threshold is 0.05 divided by 10, which is 0.005, so any single test now needs a p-value below 0.005 to count. Suppose one outcome comes back at p = 0.008. Judged the old way against 0.05 it would look significant, but 0.008 is above the corrected 0.005 threshold, so it does not survive. The same conclusion appears if you adjust the p-value instead: 0.008 times 10 is 0.08, which is above 0.05. Either way, the finding is not significant once you allow for having looked 10 times.
Related calculators
- P-Value Calculator: p-value from a test statistic.
- T-Test Calculator: compare two means.
- One Sample T-Test Calculator: mean against a target.
- Two Sample T-Test Calculator: two independent groups.
- Standard Deviation Calculator: spread of a data set.