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.

翻译：本文研究了在正态分布近独立设定下，Bonferroni方法中族系误差率（FWER）的行为。在寻找合适的相关性惩罚项时，注意到与\cite{efron2007correlation}的研究不同，在此设定下相关系数的均方根（RMS）并不适用。我们针对偏离独立性的情况提出了一个合适的修正因子，并近似得到了该近独立设定下的FWER。