Bonferroni Correction Calculator

The Bonferroni correction is a simple method for limiting false-positive findings when a study performs more than one hypothesis test. A conventional alpha of 0.05 gives each individual test a five percent chance of rejecting a true null hypothesis under its assumptions. When many tests are considered together, the chance of at least one accidental rejection can become much larger than five percent. The correction protects the family-wise error rate by dividing the desired overall alpha by the number of comparisons. If a study plans m tests and wants a family-wise alpha of α, each test is evaluated against α/m. For example, five tests with an overall alpha of 0.05 use a corrected threshold of 0.01. An observed p-value of 0.008 remains significant, while a p-value of 0.02 does not. An equivalent presentation multiplies every raw p-value by the number of tests and caps the result at one. Comparing adjusted p-values with the original alpha leads to the same decisions. The method follows the union bound, so it controls the probability of one or more type I errors without requiring the tests to be independent. That broad validity is a major strength. It is also conservative, particularly when tests are numerous or positively correlated. Conservatism means the method can reduce statistical power and make genuine effects harder to detect. Researchers should define the family of hypotheses before examining results rather than selecting a convenient number of comparisons afterward. A test family should contain hypotheses that belong to the same inferential claim or decision. For example, a trial comparing several treatment groups with one control may treat those comparisons as one family. Exploratory analyses may contain separate coherent families, but dividing them requires a scientific justification. Repeatedly testing outcomes, subgroups, time points, and model specifications without accounting for all relevant choices can still inflate false-positive risk. Bonferroni is useful when avoiding even one false claim is especially important, the number of comparisons is modest, or a transparent correction is required. Holm's sequential procedure also controls family-wise error and is usually at least as powerful. Benjamini-Hochberg controls the false discovery rate instead and may suit large exploratory screens. This calculator supplies the exact Bonferroni threshold; choosing the correction method still depends on the study design, confirmatory goals, and consequences of false positives.