Chapter 10: Dunn-Šldák Critical Values and p Values

The Dunn and Dunn- Šidák multiple comparison procedures are widely used to test hypotheses and construct confidence intervals for C ≥ 2 a priori, nonorthogonal contrasts. Dunn’s (1961) procedure is based on the additive Bonferroni inequality. The procedure controls the long-run average number of erroneous statements for a family of C contrasts, the per family error rate denoted by α_PP The per family error rate is controlled by splitting α_PF among the null hypothesis tests or confidence intervals so that $Σi=1CαPCi=αPF$⁠, where $αPCi$ is the ith per contrast type I error. Researchers often assign the same type I error to all C contrasts or confidence intervals in which case α_PC = α_PF/C. A second and slightly more powerful multiple comparison procedure was proposed by Sidák (1967) and is called the Dunn-Šidák procedure. This procedure is based on a multiplicative inequality. For any set of C a priori contrasts or confidence intervals, the procedure provides an upper bound for the familywise error rate denoted by α_FW This is the probability of making one or more erroneous statements for a family of C contrasts. To control the familywise error rate, the Dunn- Sidák procedure tests each contrast at α_PC = 1 − (1 − α_FW)^1/C. Šidák showed that the familywise error rate for C nondependent tests is less than or equal to 1 − (1 − α_PC)^C, which is always less than or equal to α_PF. For this reason, the Dunn-Šidák procedure is preferred over Dunn’s procedure when C ≥ 2.