Examining the Probabilities of Type I Error for Unadjusted All Pairwise Comparisons and Bonferroni Adjustment Approaches in Hypothesis Testing for Proportions

Abstract

The aim of this study is to examine the association among the probabilities of Type I error obtained by Unadjusted All Pairwise Comparisons (UAPC) and Bonferroni-adjustment approaches, the sample size and the frequency of occurrence of an event (prevalence, proportion) in hypothesis testing of difference among the proportions in studies. In the simulation experiment planned for this purpose, 4 groups were formed and the proportions in each group were chosen between 0.10 and 0.90 so that they will be equal at each experiment. Furthermore, the sample sizes were chosen from 20 to 1000. In accordance with these scenarios, the probabilities of Type I error were calculated by both of approaches. In each approach, a significant S-curve relationship was found between the probability of Type I error and sample size. However, a significant quadratic relationship was found between the probabilities of Type I error and the proportions in each group. Nonlinear functional relations were put forward in order to estimate the observed Type I error rates obtained by the two different approaches where sample size and the proportion in each group are known. Furthermore, it was founded that Bonferroni-adjustment approach cannot always protect Type I error level. It was observed that the probability of Type I error estimated by the functional relation on Type I error rate for UAPC approach is lower than the values calculated using the formula in the literature.