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

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.