Editing Biostatistics (section)

=== Multiple testing ===

In multiple tests of the same hypothesis, the probability of the occurrence of [[False positives and false negatives|false positives]] [[Family-wise error rate|(familywise error rate)]] increase and a strategy is needed to account for this occurrence. This is commonly achieved by using a more stringent threshold to reject null hypotheses. The [[Bonferroni correction]] defines an acceptable global significance level, denoted by α* and each test is individually compared with a value of α =  α*/m. This ensures that the familywise error rate in all m tests, is less than or equal to α*. When m is large, the Bonferroni correction may be overly conservative. An alternative to the Bonferroni correction is to control the [[False discovery rate|false discovery rate (FDR)]]. The FDR controls the expected proportion of the rejected [[Null hypothesis|null hypotheses]] (the so-called discoveries) that are false (incorrect rejections). This procedure ensures that, for independent tests, the false discovery rate is at most q*. Thus, the FDR is less conservative than the Bonferroni correction and have more power, at the cost of more false positives.<ref>Benjamini, Y. & Hochberg, Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological) 57, 289–300 (1995).</ref>