Bonferroni Correction Calculator - Adjust Significance for Multiple Comparisons

The Bonferroni correction calculator adjusts significance thresholds and p-values when you run several hypothesis tests on the same dataset, so the chance of at least one false positive stays under your chosen family-wise error rate. It is the most widely used tool for guarding against spurious significant results in ANOVA post-hoc tests, GWAS screens, A/B/n experiments, neuroimaging studies, and clinical trials with multiple endpoints. Enter the number of comparisons, the family-wise α, and an optional p-value to see the corrected threshold, the adjusted p-value, and whether that p would survive the correction.

• • ANOVA post-hoc tests: Compare every pair of group means after a significant omnibus ANOVA without inflating the chance of any spurious pairwise difference.
• • GWAS and genomics screens: Apply a stringent per-SNP threshold across hundreds of thousands of associations to limit genome-wide false discoveries.
• • A/B/n experiments: Test several marketing, product, or pricing variants at once while keeping the rollout-wide false-positive rate at the chosen α.
• • Clinical trials with multiple endpoints: Evaluate several primary and secondary endpoints while controlling the family-wise Type I error rate required by regulators.

The calculator mirrors the original Bonferroni (1935/1936) inequality, which bounds the probability that at least one of n events occurs by the sum of their individual probabilities. That bound holds for independent and correlated events, so Bonferroni control of the family-wise error rate does not require independence. The correction simply divides α by n, giving a stricter per-test threshold, which is why reviewers and journal style guides still recommend it for confirmatory work.

Leave the p-value field at its default to get the adjusted threshold for a planned study. Enter the observed p-value from one of your tests if you already ran them and want to know whether it survives the correction. Report the result with the adjusted p-value rather than as a discovery, and remember that a non-significant corrected p does not prove the original finding was a false positive, only that it does not clear the stricter bar you chose.

Pair this Bonferroni correction calculator with our T-Test Calculator to plan the per-comparison threshold for every pairwise mean comparison after a significant ANOVA.

The calculator uses two related formulas that scale the family-wise error budget across all comparisons. The classic Bonferroni correction divides the family-wise α by the number of tests, while Sidak uses a multiplicative adjustment that assumes independent tests. For a single observed p-value, the same scaling produces an adjusted p-value that can be compared directly to the original α.

• n: Number of comparisons in the family. Must be a positive integer; values above 100 give very small α'.
• α (alpha): Target family-wise Type I error rate. Most fields use 0.05; regulatory or exploratory work can pick 0.01 or 0.10.
• p (p-value): Observed p-value from one of the tests. Used only to compute the adjusted p and the significance flag.
• Method: Bonferroni is the standard α / n rule. Sidak uses the formula above and is slightly less conservative under independence.

Both corrections come from the Bonferroni inequality, which upper-bounds the probability of any false positive in a family of tests. Tightening each per-test threshold from α to α' keeps the worst-case family-wise error at or below the target. The adjusted p-value applies the same logic to a single observation.

Results update in real time. Switch between Bonferroni and Sidak, or change n and α, to compare scenarios on the fly.

According to the R `p.adjust` reference manual, the Bonferroni correction multiplies each raw p-value by the number of comparisons, and several step-down alternatives (Holm, Hochberg, Hommel) and false-discovery-rate methods (Benjamini-Hochberg, Benjamini-Yekutieli) are available when stricter control loses too much power.

According to the NIST/SEMATECH e-Handbook of Statistical Methods (Bonferroni's method), Bonferroni applies to any finite set of pre-selected contrasts, is valid for equal or unequal sample sizes, and keeps the overall confidence coefficient at least 1 - α by tightening each interval to 1 - α/g.

If you need to convert a z-score or t-score into a raw p-value before adjusting it, use our P-Value Calculator alongside this Bonferroni correction calculator.

These four ideas underpin every multiple-comparisons adjustment. Read them once and the outputs of any post-hoc or multi-endpoint analysis will make sense.

When a paper reports an "α = 0.05 after Bonferroni correction" for n = 20 tests, each test used a threshold of 0.0025. This tool reproduces that math and lets you change n or α to see how the conclusion would shift.

To report effect sizes that survive multiple comparisons, pair this calculator with our Confidence Interval Calculator for the confidence intervals that complement each adjusted p.

Use the calculator whenever you need to decide whether a set of results can stand as significant or whether some p-values are inflated by chance. The four steps below cover the common case of post-hoc pairwise comparisons.

1. 1 Enter the number of comparisons: Type the count n of hypothesis tests in the family (for example 6 pairwise comparisons after a one-way ANOVA with 4 groups).
2. 2 Set the family-wise α: Pick the overall Type I error rate you tolerate. Most studies use 0.05; regulatory submissions often use 0.01.
3. 3 Choose Bonferroni or Sidak: Default to Bonferroni when tests may be correlated. Pick Sidak for slightly more power when tests are independent.
4. 4 Add the observed p-value: Enter the p from one of your tests. The calculator returns α', the adjusted p-value, and whether the result survives correction.
5. 5 Read the expected false positives: The expected FP field shows how many spurious significant results you would see at the uncorrected α, a useful sanity check when n is large.

Suppose a clinical trial tests 8 endpoints at α = 0.05. Enter n = 8, α = 0.05, method Bonferroni, and read α' = 0.00625. Each endpoint needs p < 0.00625 to be declared significant. If your smallest endpoint p is 0.012, the adjusted p becomes 0.096, so the endpoint is no longer significant. The expected false-positive count at the uncorrected α is 8 × 0.05 = 0.40, confirming why a correction is needed.

For large-sample tests where the z approximation is acceptable, run the raw p through our Z-Score Calculator before applying the Bonferroni correction.

The calculator turns a one-line textbook formula into a live decision tool that researchers and students can use on any device. The benefits below explain why it earns a place in your standard analysis workflow.

• • Live corrected thresholds: Get the per-test α' in milliseconds without rewriting the α / n formula in a notebook.
• • Side-by-side Bonferroni and Sidak: Compare the conservative Bonferroni and the slightly less strict Sidak correction in the same view to judge whether the difference matters for your n.
• • Adjusted p-value with significance flag: See the scaled p-value and a clear pass/fail signal, so you do not have to mentally compare the raw p against the corrected threshold.
• • Expected false-positive count: Quantify the multiple-comparisons problem with n × α so non-statistician collaborators can see why the correction matters.
• • Free and runnable in the browser: No installation, no license, no upload of sensitive data. Useful for teaching assistants, peer reviewers, and quick sanity checks.
• • Pairs with related calculators: Use it alongside the p-value, t-test, chi-square, and confidence interval calculators to cover the full hypothesis-testing workflow.

Categorical comparisons across many contingency tables also need correction, so this Bonferroni correction calculator pairs naturally with our Chi-Square Calculator.

Three inputs drive the output and a few conventions decide how to interpret them. Use the factors below to pick sensible defaults before trusting a Bonferroni result.

• • Bonferroni is conservative. With n in the hundreds or thousands, the per-test threshold becomes so small that true positives are hard to detect; step-down (Holm-Bonferroni) or false-discovery-rate methods (Benjamini-Hochberg) usually retain more power.
• • The expected false-positive count n × α is a planning average, not a hard ceiling. With n = 100 and α = 0.05 you expect about 5 spurious hits, but the observed count depends on the random sample, which is why the correction is a probabilistic safeguard rather than a deterministic cap.

According to the R `p.adjust` reference manual (Holm, Hochberg, Hommel, BH, BY methods), Holm's step-down method is at least as powerful as Bonferroni and remains valid under arbitrary dependence assumptions, so it is the preferred FWER alternative when Bonferroni is too conservative.

For discrete distributions such as the binomial, the Bonferroni correction works alongside our Continuity Correction Calculator so each comparison uses both normal approximation and a multiple-testing safeguard.