Control false discovery rate or family-wise error when testing many hypotheses at once.
When you conduct many statistical tests simultaneously — for example, comparing 20 brain regions, 100 genes, or 30 correlation pairs — the probability of obtaining at least one false positive by chance alone becomes very high. With α = .05 and 20 tests, the family-wise error rate is approximately 64%. Multiple testing correction methods control this inflation.
The Bonferroni correction is the most conservative: it divides α by the number of tests, ensuring the family-wise error rate stays at or below 5%. The Holm-Bonferroni method is uniformly more powerful than Bonferroni. The Benjamini-Hochberg procedure controls the False Discovery Rate (FDR) — the expected proportion of false positives among rejected hypotheses — making it the preferred method in large-scale exploratory research such as genomics, neuroimaging, and epidemiology.
StatRyx accepts a list of p-values, applies the selected correction method, and returns adjusted p-values, significance decisions at α = .05, and a visualisation showing original vs. adjusted p-values across all tests.
Every test at α = .05 carries a 5% chance of a false positive, so running 20 tests makes at least one false positive likely (about 64% if the tests are independent). Corrections control this in two ways. Family-wise error methods (Bonferroni, Holm) keep the chance of any false positive at 5%; false discovery rate methods (Benjamini–Hochberg) keep the expected share of false positives among significant results at 5%, which preserves more power when many tests are run.
| Comparison | p (raw) | p_adj (BH) | Significant? |
|---|---|---|---|
| Group A vs B | .003 | .045 | Yes |
| Group A vs C | .012 | .090 | No |
| Group B vs C | .001 | .030 | Yes |
| Group A vs D | .048 | .144 | No |
To control the family-wise error rate across 15 comparisons, Holm-Bonferroni correction was applied. Eight comparisons remained significant after correction (p_adj < .05), while seven were no longer significant. The false discovery rate, estimated using the Benjamini-Hochberg procedure, was maintained at q < .05.
Use Bonferroni or Holm when controlling family-wise error is critical (clinical trials, confirmatory research). Use Benjamini-Hochberg FDR for exploratory research (genomics, large-scale surveys). Holm is always at least as powerful as Bonferroni.
For correlation matrices, you can enable auto-correction (FDR). For other analyses, ask the AI to apply correction to a specific set of p-values.
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
Say which correction was applied and to how many tests, then report the adjusted p-values: "Holm–Bonferroni correction was applied to the 15 pairwise comparisons; eight remained significant (adjusted ps < .03)."
Holm's method controls the same family-wise error rate as Bonferroni but is uniformly more powerful, so there is rarely a reason to prefer plain Bonferroni. Bonferroni is simpler to explain: divide α by the number of tests.
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