Playing Safe with Misweighted Means
本文证明在方差不相等的情况下，学生t统计量是一种宽容或安全的统计量；对于任何加权均值，都存在对应的加权离差平方和，可构造安全的类t检验统计量，表明权重选择不必非常精确，只要通过加权离差平方和进行补偿即可。
Abstract This article concludes that Student's t statistic is a forgiving or safe statistic in the presence of unequal variances. More generally, for every weighted mean , there is a corresponding weighted sum of deviations squared S w,0 2, which together with the mean defines a safe Student-like test statistic. These results imply that the choice of weights in need not be all that precise, provided a compensation is made via S w,0. Such is the case in the example considered. Key Words: Asymptotic normalityDegrees of freedomInhomogeneity of varianceMisweightingSafe test statisticsStudent's t.