How this calculator works
Bonferroni divides the desired family error limit by the total number of planned tests. Equivalently, multiply each raw p-value by that count and cap the result at one. The Bonferroni bound holds without assuming independent tests, but can be conservative. Sidak uses the product rule for independent tests and is slightly less conservative. Reverse modes recover a family error level or the largest whole test count compatible with a supplied per-test threshold. Include all tests in the chosen family, including those whose p-values you do not enter here. The confidence output is the individual confidence level for simultaneous Bonferroni intervals.
Formula
Bonferroni: αindividual = αfamily/m; padjusted = min(1, mp). Sidak: αindividual = 1 - (1 - αfamily)^(1/m); padjusted = 1 - (1 - p)^m. Invert these relationships for αfamily or m.
Worked example
For five tests and family alpha 0.05, the per-test threshold is 0.01. Raw p = 0.001 becomes 0.005 and is significant; p = 0.02 becomes 0.10 and is not.
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Frequently asked questions
Must tests be independent?
Bonferroni works without independence. The Sidak calculation here assumes independent tests; do not assume it controls arbitrary dependent tests.
What counts as a family?
Specify the collection of claims whose chance of at least one false rejection you want to control, preferably before seeing results.
Can I enter only some p-values?
Yes, but the test count must still include the entire family. Entering fewer results does not reduce that count.