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Statistics

Bonferroni correction calculator

Adjusts the significance threshold when running many statistical tests at once.

What this calculator does

Bonferroni correction works out adjusts the significance threshold when running many statistical tests at once. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

FormulaAdjusted α = α / m; probability of at least one false positive without correction = 1 − (1−α)ᵐ

The inputs explained

FieldWhat to enter
Family-wise significance level (α) (%)A number, measured in %. Starts at 5.
Number of comparisons (m)A number. Starts at 10.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with family-wise significance level (α)

Every other input is held at the calculator’s starting values while family-wise significance level (α) varies. Select any row to load that scenario into the calculator.

How the answer changes with family-wise significance level (α)
Family-wise significance level (α) (%)Bonferroni-adjusted α per testComparisonsChance of ≥1 false positive if uncorrected
2.50.250%1022.4%
3.750.375%1031.8%
50.500%1040.1%
7.50.750%1054.1%
101.00%1065.1%
151.50%1080.3%