两个非正态样本同分布检验的非参数法选择

Selection of Nonparametric Tests When Comparing the Homogeneity of Two Non-normal Distributions

目的对检验两个非正态样本是否同分布的常用非参数方法进行评价,为合理选择检验方法提供参考依据。方法采用Matlab7.5软件编程,模拟数据在不同的分布类型、样本量相等或不等、方差齐或不齐、方差与样本量顺向或反向、均数相等或不等等条件下,分别采用Wilcoxon检验、Wald-Wolfowitz游程检验(WWR)、Kolmogorov-Smirnov检验(K-S)和Hollander极端反应检验(Hollander)进行检验。结果给出4种检验法的Ⅰ型和Ⅱ型误差估计值。结论当两个总体均数相等时,建议选用Hollander检验;当两个总体方差相等时,建议选用Wilcoxon检验或K-S检验;而在两个总体方差、均数都不相等但差异不大时,则可选用Wilcoxon检验、K-S检验或Hollander检验中的任意一种。

ObjectiveThe study was attempted to evaluate four nonparametric tests when comparing the homogeneity of two non-normal distribution,so as to offer some guidance for the selection of method. MethodsWith MATLAB,simulation experiments were performed under different distributions,variances,means,sample sizes,and large variance to large sample size or large variance to small sample size,etc.Wilcoxon test,Wald-Wolfowitz runs test,Kolmogorov-Smirnov test,and Hollander extreme test were conducted to compute type Ⅰ error and type Ⅱ error estimates. ResultsType Ⅰ error and type Ⅱ error estimate of four tests were given. ConclusionHollander extreme test is appropriate to the samples with equal mean;Wilcoxon test or Kolmogorov-Smirnov test is selected to the samples with equal variance;Wilcoxon test,Kolmogorov-Smirnov test and Hollander extreme test are all recommended when their variances and means are unequal,but not clearly different.