How to use it
- Paste the p-values of all the tests in the family, for example
0.008, 0.04, 0.03, 0.005, 0.2. - Set α and choose the method for the decision.
- Read how many tests stay significant and which ones (#1 is the first p-value you entered). Every method’s adjusted p-values are listed in the input order.
How the corrections work
Let m be the number of tests and p₍₁₎ ≤ p₍₂₎ ≤ … the sorted p-values.
- Bonferroni: min(1, m·p).
- Šidák: 1 − (1 − p)^m, slightly less strict than Bonferroni for independent tests.
- Holm: min(1, (m − i + 1)·p₍ᵢ₎), then made non-decreasing from the smallest p upward.
- Hochberg: the same products, made non-increasing from the largest p downward; valid for independent or positively dependent tests.
- Benjamini–Hochberg: min(1, m·p₍ᵢ₎/i), made non-increasing from the largest p downward.
A test is significant when its adjusted p ≤ α.
Worked example
Five p-values 0.008, 0.04, 0.03, 0.005, 0.2 at α = 0.05.
- Bonferroni: 0.04, 0.2, 0.15, 0.025, 1 — tests #1 and #4 are significant (threshold 0.01).
- Holm: sorted 0.005, 0.008, 0.03, 0.04, 0.2 times 5, 4, 3, 2, 1 gives 0.025, 0.032, 0.09, 0.08, 0.2; the running maximum makes the fourth 0.09. In input order: 0.032, 0.09, 0.09, 0.025, 0.2 — again #1 and #4, so 2 / 5.
- Benjamini–Hochberg: 5p/rank = 0.025, 0.02, 0.05, 0.05, 0.2, and the running minimum from the top gives 0.02, 0.05, 0.05, 0.02, 0.2 — tests #1, #2, #3 and #4 pass.
Tips and common mistakes
- Decide on the family of tests before looking at the results, and include every test in it, not just the promising ones.
- Bonferroni is very conservative with many tests; Holm is a free improvement with the same guarantee.
- Do not mix methods: report the one you chose and its adjusted p-values.