Multiple Comparisons Problem
When conducting multiple statistical tests, the probability of obtaining at least one false positive by chance increases with the number of tests. The multiple comparisons problem (also called the multiplicity problem) occurs because if you conduct 100 hypothesis tests at α = 0.05, you expect ~5 false positives by chance alone, even if all null hypotheses are true. Correction methods—Bonferroni, Benjamini-Hochberg false discovery rate (FDR), and others—adjust the significance threshold or p-values to control error rates. This concept is critical for research integrity and has profound implications for exploratory science.
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- Bonferroni, C. E. (1935). Il calcolo dei coefficienti di correlazione nel caso di variabilità di gruppi. Instituto Italiano di Statistica. · URL
- Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57(1), 289–300. · DOI 10.1111/j.2517-6161.1995.tb02031.x
- Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124. · DOI 10.1371/journal.pmed.0020124
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