A comprehensive error rate for multiple testing

Details A comprehensive error rate for multiple testing A comprehensive error rate for multiple testing

2011-12-19

arxiv.org/abs/1112.4519v1

Mathematics

Statistics Theory

Scientific paper

In multiple testing, a variety of metrics have been introduced to control the false discoveries occurrences such as the Family-Wise Error Rate (FWER), the False Discovery Rate (FDR), the False Exceedence Rate (FER), etc. We present a way to combine and extend these metrics and show how to control them. The new concept considers the relationship between the number of rejections and the number of false positives by introducing a quantity defined by the number of false positives divided by a function of the number of rejections. We call this quantity the Scaled False Discovery Proportion (SFDP). This quantity is used to define two new false positive metrics: the Scaled Tail Probability (STP) and the Scaled Expected Value (SEV). We give procedures that control these two new error rates under different assumptions. With some particular cases of the scaling function, these two metrics cover well known false positives metrics such as the FWER, the k-FWER, the FDR, the FER and many others. We also propose some examples of scaling functions that could be appropriate in different fields of application depending on the level of conservativeness that the user wishes to reach.

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