比较两组样本均值的随机加权法

A Random Weighting Method for the Comparison of the Means of Two Independent Samples

利用随机加权法给出了两组相互独立的样本均值比较的假设检验,这种检验并不要求被检样本分布一定是正态的,同时证明在适当条件下所用的估计比通常的正态逼近具有更高的精度。

Suppose X1,X2, … ,Xm and Y1, Y2,…, Yn are samples from two independent populations with EX1 = μ1, EY1 = μ2, VarX1 = σ12 and VarY1=σ22. Using the random weighting method, an estimation of the distribution of the statisticTm+n=X-Y/(σ12/m+σ22/n)1/2is given when μ1 = μ2 It is further proved that the estimation is more accurate than the estimation using normal distribution to approximate the distribution of Tm+n. Using this estimation, a method is given for the comparison of the means of two independent set of samples when the distributions of the samples are not normal.