Observation on F.W.E.R. and F.D.R. for correlated normal

TL;DR

This paper investigates how correlation among normal variables affects the control of FWER and FDR in multiple testing procedures, revealing their conservative nature under positive correlation and suggesting potential for power improvement.

Contribution

It provides a simulation-based analysis of FWER and FDR behavior under equicorrelation, highlighting their conservative control and opening avenues for adjustment methods.

Findings

F.W.E.R. is concave for few hypotheses, then convex with increasing correlation.

Procedures control error rates more conservatively under positive correlation.

Potential for power enhancement by adjusting for correlation.

Abstract

In this paper, we have attempted to study the behaviour of the family wise error rate (FWER) for Bonferroni's procedure and false discovery rate (FDR) of the Benjamini-Hodgeberg procedure for simultaneous testing problem with equicorrelated normal observations. By simulation study, we have shown that F.W.E.R. is a concave function for small no. of hypotheses and asymptotically becomes a convex function of the correlation. The plots of F.W.E.R. and F.D.R. confirms that if non-negative correlation is present, then these procedures control the type-I error rate at a much smaller rate than the desired level of significance. This confirms the conservative nature of these popular methods when correlation is present and provides a scope for improvement in power by appropriate adjustment for correlation.