Bonferroni Correction Calculator

The Bonferroni correction is a statistical adjustment used to control the family-wise error rate (FWER) when performing multiple hypothesis tests simultaneously. When you run m independent tests each at α = 0.05, the probability of at least one false positive is 1 − (0.95)^m — with 20 tests, that probability jumps to 64%, meaning you are more likely than not to declare a spurious significant result. The Bonferroni correction prevents this by dividing α by the number of tests: α_adj = α / m.

This calculator goes beyond simple Bonferroni correction. It also provides the Sidak correction (α_sidak = 1 − (1−α)^(1/m)), which is slightly less conservative, and Holm's step-down procedure, which is uniformly more powerful than Bonferroni while still controlling FWER. When you enter actual p-values, the calculator displays adjusted p-values and significance verdicts for each test, plus summary counts of how many tests survive each correction method.

Each correction method adjusts the significance threshold differently. Bonferroni is the simplest and most conservative; Sidak is mathematically derived for independent tests; Holm's procedure applies a step-down approach that is more powerful.

When you enter actual p-values, the calculator provides a comprehensive table showing how each test fares under different correction methods. Understanding this table helps you make informed decisions about which results remain credible after adjusting for multiplicity.

Holm's method works by sorting p-values from smallest to largest, then comparing each against α/(m−k+1). The first non-significant result stops the procedure, and all subsequent tests are deemed non-significant regardless of their raw p-values. This sequential approach consistently identifies more true positives than Bonferroni while maintaining strict FWER control.

Using the multiple comparison correction calculator:

1. Set the original alpha: Choose your family-wise significance level — 0.05, 0.01, 0.10, or 0.001 from the dropdown. This is the overall probability of making at least one Type I error across all tests.
2. Enter p-values (optional): Provide comma-separated p-values from your individual hypothesis tests. The calculator will adjust each one and show which survive correction. If you do not enter p-values, provide the number of tests below.
3. Or enter number of tests: If you have not yet computed p-values but want to determine the adjusted alpha threshold, simply enter the total number of comparisons you plan to make.
4. Read the results: The calculator displays adjusted alphas for Bonferroni and Sidak, plus a detailed p-value table with Bonferroni-adjusted values and Holm significance verdicts when p-values are provided.

Multiple comparison corrections are essential in genomics and bioinformatics, where researchers routinely test thousands or millions of genetic variants for association with disease. Without correction, massive studies would produce oceans of false positives. The Bonferroni correction is standard in genome-wide association studies (GWAS), where the significance threshold is typically set at 5 × 10⁻⁸ after adjusting for roughly one million independent tests.

In clinical trials, multiple comparison corrections apply when analyzing multiple endpoints, comparing multiple dose groups to a placebo, or conducting interim analyses. Regulatory agencies like the FDA require pre-specified multiplicity adjustment plans to ensure the overall Type I error rate does not exceed 5%. In psychology and neuroscience, corrections are required when analyzing multiple brain regions, time points, or behavioral measures in the same study.

In A/B testing and digital marketing, running multiple variants against a control without correction inflates the false discovery rate. Companies testing 10 landing page variants at α = 0.05 would expect about 40% chance of at least one false positive — leading to misguided business decisions based on random noise.