Carlo Bonferroni

Bonferroni correction allocates the available significance level across the full set of comparisons. If the chosen level is α and the analysis contains n tests, each test is assessed at α/n, creating a stricter threshold than when a single test is considered alone. This allocation reduces the chance that the testing set produces a false positive.

Instead of changing the threshold, the same adjustment can be expressed through p-values: each individual p-value is adjusted to reflect the number of comparisons, then interpreted against the chosen significance level. These two presentations communicate the same safeguard in different formats, allowing results to be reported as either comparison-specific thresholds or adjusted significance measures.

Bonferroni’s main trade-off is conservatism. By requiring stronger evidence across a set of tests, it lowers the likelihood that the collection will contain a false-positive finding, but it can also make statistical significance harder to obtain. The correction is therefore useful when limiting false positives across several simultaneous conclusions is more important than using a less restrictive threshold.

The number of comparisons directly determines the correction. As more hypotheses are evaluated together, dividing the chosen significance level by a larger number produces a smaller per-test threshold. Consequently, the adjustment must reflect the full set of comparisons relevant to the analysis rather than applying the same unadjusted threshold independently to every hypothesis.

Researchers first specify the significance level and identify how many hypotheses or comparisons will be evaluated. They then divide the level by that count, or adjust the individual p-values instead. Each result is interpreted using the selected form of adjustment, keeping conclusions consistent across the simultaneous tests and reducing the likelihood of a false-positive set-level finding.

Bonferroni correction is used when an analysis examines several hypotheses at once, such as comparisons among treatment groups or relationships involving multiple variables. In these settings, the question is not only whether one result appears significant, but whether the set of reported findings remains protected against a false positive. The correction supplies that family-wise safeguard.

A result that meets the corrected threshold is judged significant within the broader collection of tests, rather than under an isolated comparison. Results that do not meet the corrected criterion should not be treated as significant under that family-wise analysis, even if an unadjusted p-value appears small. This interpretation keeps conclusions aligned with the multiple-testing adjustment.