Multiple comparisons p-value correction
Adjust several p-values with Bonferroni, Holm or Benjamini–Hochberg corrections.
A clear answer. Here’s how.
Bonferroni multiplies each p by the number of tests m. Holm sorts the p-values and multiplies the i-th smallest by (m − i + 1), keeping adjusted values non-decreasing. Benjamini–Hochberg multiplies the i-th smallest by m ÷ i and keeps values non-decreasing from the largest down. Every adjusted value is capped at 1. The first two control the chance of any false positive; BH controls the expected share of false discoveries among the results declared significant.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- P-values, one per line (optionally “label: p”)
Gene A: 0.01 Gene B: 0.04 Gene C: 0.03 Gene D: 0.005
- Significance level α
- 0.05
- Method used for the significance column
- Holm (step-down, family-wise)
Example result
| Test | Raw p | Bonferroni | Holm | Benjamini–Hochberg | Significant at α = 0.05 (Holm) |
|---|---|---|---|---|---|
| Gene A | 0.01 | 0.04 | 0.03 | 0.02 | Yes |
| Gene B | 0.04 | 0.16 | 0.06 | 0.04 | No |
| Gene C | 0.03 | 0.12 | 0.06 | 0.04 | No |
| Gene D | 0.005 | 0.02 | 0.02 | 0.02 | Yes |
Bonferroni and Holm control the chance of any false positive (family-wise error); Benjamini–Hochberg controls the expected share of false discoveries and assumes independent or positively dependent tests. Adjusted values are capped at 1 and compared with α. Holm is never less powerful than Bonferroni.