Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER

In a multiple testing setting, the investigator is faced with choosing a method for controlling the Type I error rate. In this manuscript, we derive and compare the exact distribution for the number of false positives under a commonly used distribution. The results from this work can be extended to derive the distribution of other error control quantities, while the conclusions from our simulations can be used to power future studies.