Fuzzy Method for Multiple Hypotheses Testing Procedure

Multiple hypotheses testing is a procedure for testing many hypotheses simultaneously which can control familywise error rate (FWER). The primary method was proposed by Bonferroni and it is the most popular among all procedures for controlling FWER. Many multiple hypothesis tests have been developed by changing a constant in each testing step including the Hochberg method and Bonferroni–Sidak method. These multiple hypotheses modification methods are more powerful than the classic Bonferroni’s method and they still focus on controlling the FWER. However, there is an alternative method to improve the multiple hypotheses testing procedures without changing their critical value sets, which is called a fuzzy method. In this study, the fuzzy method will be applied to the Bonferroni method, the Hochberg method and the Bonferroni–Sidak method. The power of the original multiple hypotheses testing method and the fuzzy multiple hypotheses testing method are compared by simulation study using the R program.