Multiple-Comparisons Corrections

Step 1 — Enter your p-values

Instructions:

Paste one p-value per line. Optionally prefix with a label and a comma (e.g. Outcome A, 0.017).
Values must be in [0, 1]. Scientific notation (1.2e-4) is fine.
Or click Load recent results to pull p-values from tests you ran earlier in this session.

P-values (one per line; optional label + comma prefix):

Significance threshold (α):

Step 2 — Adjusted p-values

Rows are sorted by raw p-value ascending. Cells shaded green reject the null under that method at the chosen α.

Rank	Label	Raw p	Bonferroni	Holm	BH (FDR)	Reject under

Step 3 — Visualize the inflation

Family-wise error rate (FWER) for k independent tests at level α: FWER = 1 − (1 − α)^k. Bonferroni flattens this by testing each individual hypothesis at α / k.

α for chart: 0.050 Uncorrected Bonferroni Your k

Which correction should I use?

Bonferroni

p_adj = min(1, p × k)

Controls: FWER (family-wise error rate).

Use when: you want a simple, universally understood correction and you can afford to lose power. Safe default for a small number of pre-planned confirmatory tests.

Downside: very conservative when k is large or tests are correlated.

Holm-Bonferroni

p_adj(i) = max_j≤i [(k − j + 1) · p_(j)]

Controls: FWER, uniformly more powerful than Bonferroni.

Use when: you want strict FWER control but don't want Bonferroni's power loss. No reason not to prefer it over plain Bonferroni.

Interpretation: sequentially rejective — the smallest p is tested at α/k, the next at α/(k−1), etc.

Benjamini-Hochberg

p_adj(i) = min_j≥i [p_(j) · k / j]

Controls: FDR (false discovery rate — expected proportion of rejected nulls that are false).

Use when: you have many tests (screening, omics, exploratory epi) and can tolerate a small rate of false positives among your discoveries.

Downside: a discovery can be “approximately true” — not the right tool when one false positive is catastrophic.

Biostats rule of thumb: Confirmatory trials with pre-registered endpoints → Holm. Screening across many candidate biomarkers or SNPs → BH. Regulatory / primary-endpoint analysis that must not leak a single false positive → Bonferroni (or a formal gatekeeping procedure).

Worked example — five endpoints in a clinical trial

A small RCT tests five secondary endpoints against placebo. The raw p-values come back as p₁ = 0.003, p₂ = 0.013, p₃ = 0.018, p₄ = 0.041, p₅ = 0.120. At α = 0.05, how many “survive” a correction?

Uncorrected: four significant (p₁–p₄). But the expected number of false positives under the null is k·α = 0.25.
Bonferroni (α/k = 0.010): only p₁ clears the bar.
Holm: p₁ vs 0.010 ✓, p₂ vs 0.0125 ✗ — stops there. One discovery.
BH at q = 0.05: p₃ ≤ (3/5)(0.05) = 0.030 ✓, so everything up to rank 3 is discovered. Three discoveries.

Click Load example above to see the full table and the inflation curve for this scenario.