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Bonferroni & Šidák Per-Test Significance Thresholds

Convert a chosen family-wide significance level to a per-test threshold using Bonferroni or Šidák.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For four tests and a 5% family-wide level, the Bonferroni per-test threshold is 0.0125, equivalent to 1.25%.

Bonferroni threshold = α/m; Šidák threshold = 1 − (1 − α)^(1/m)

Worked example

Enter these known values and leave the other values blank.

Threshold method
Classic Bonferroni correction
Positive whole number of tests
4 tests
Bonferroni family-wide significance level
5 %
Bonferroni per-test threshold as a fraction
0.0125

Assumptions and limitations

  • Choose the family of tests before applying a correction. Test count is a positive integer; family-wide levels are strictly between zero and one.
  • Bonferroni supports arbitrary dependence through the union bound. The exact Šidák family-wide relation assumes independent tests; dependence needs separate justification.
  • The retained Bonferroni input is a percentage, while the Šidák input and both outputs are fractions. For example, 0.05 means 5% in a fraction field.
  • These are rejection thresholds, not adjusted observed p-values. The two modes have separate family-level inputs; switching mode does not transfer their values.

Common questions

Where do I enter an observed p-value?

These fields calculate a significance threshold from a family-wide error level. Compare observed p-values with the resulting per-test threshold; they are not inputs to a p-value adjustment here.

What happens for one test?

Both methods return the same per-test threshold as the supplied family-wide level.

References

Bookify permits an unchanged threshold when the family contains one test and identifies the two methods and input scales explicitly.

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