bonferroni adjustment calculator

What is a Bonferroni adjustment?

The Bonferroni adjustment is a simple way to reduce false positives when you run many statistical tests at once. If you test enough hypotheses, some will look significant just by chance. Bonferroni corrects for this by making the significance threshold stricter.

The core formula is straightforward: adjusted α = α / m, where α is your overall acceptable Type I error (often 0.05), and m is the number of tests.

How this calculator works

Step 1: Set your family-wise alpha

This is your total false-positive budget across all tests. Most people use 0.05, but you can use any value between 0 and 1.

Step 2: Enter the number of comparisons

This is the number of hypothesis tests you performed (or plan to interpret together). The more tests you run, the stricter the corrected threshold becomes.

Step 3: Optionally add p-values

If you paste your p-values, the calculator will compute:

• Bonferroni-adjusted p-values: p_adj = min(p × m, 1)
• Whether each test is significant against the adjusted threshold

Quick interpretation guide

• If p ≤ α/m, the result is significant under Bonferroni control.
• If p > α/m, it does not pass Bonferroni correction.
• Adjusted p-values can be compared directly to your original α (e.g., 0.05).

Example

Suppose you run 20 tests and want a family-wise error rate of 0.05. Your Bonferroni threshold is 0.05 / 20 = 0.0025. A p-value of 0.01 might look significant in an uncorrected analysis, but it is not significant after correction.

When to use Bonferroni (and when to be careful)

Good use cases

• Small to moderate number of planned comparisons
• High cost of false positives
• Confirmatory analyses where strict control matters most

Potential limitation

Bonferroni can be conservative, especially with many correlated tests, which may increase false negatives. In exploratory workflows, some researchers prefer alternatives like Holm-Bonferroni or Benjamini-Hochberg (FDR control).

FAQ

Do I need exactly as many p-values as tests?

Not necessarily for the threshold calculation itself. The threshold only needs α and m. If you provide p-values, the tool still evaluates them using the entered m value.

Is Bonferroni the same as dividing each p-value?

You can either divide alpha by m or multiply each p-value by m (capped at 1.0). These are equivalent decision rules.

Can I use this for A/B tests, biomarker panels, or survey subscales?

Yes. Any setting with multiple hypothesis testing can use Bonferroni as a conservative correction method.