  In this paper, we have attempted to study the behaviour of the family wise
error rate (FWER) for Bonferroni's procedure in a nearly independent setup for
normal distribution. In search for a suitable correlation penalty, it has been
noted that the root mean square (RMS) of correlations is not appropriate under
this setup as opposed to the study of \cite{efron2007correlation}. We have
provided a suitable correction factor for deviation from independence and
approximated the FWER under this nearly independent setup.
