Multiple Comparisons Calculator

This calculator applies three widely-used methods for adjusting p-values when performing multiple hypothesis tests simultaneously. Family-Wise Error Rate (FWER) methods — Bonferroni and Holm — control the probability of making even one false positive across all tests: Bonferroni: The simplest correction. Each p-value is multiplied by the number of tests (n). Adjusted p = min(1, p × n). While easy to understand, it is the most conservative method and can miss real effects when n is large. Holm (Step-Down): A sequential improvement over Bonferroni. P-values are sorted in ascending order. The smallest p-value is multiplied by n, the next by n-1, and so on. Monotonicity is enforced (each adjusted p-value must be at least as large as the previous). Holm is uniformly more powerful than Bonferroni while maintaining the same FWER guarantee. False Discovery Rate (FDR) method — Benjamini-Hochberg — controls the expected proportion of false positives among rejected hypotheses: Benjamini-Hochberg: P-values are sorted ascending and assigned ranks. Adjusted p_i = p_i × n / rank_i, with monotonicity enforced from the largest to smallest. This method is less conservative than FWER methods and is preferred in exploratory analyses where some false positives are acceptable as long as the overall proportion is controlled. All methods guarantee that the adjusted p-value is always between the original p-value and 1.