完全随机设计两样本的Wilcoxon检验与K-S检验功效比较

A Comparison of the Power of the Wilcoxon Rank-Sum Test and K-S Test on Completely Randomized Design of Independent Samples

目的对完全随机设计下两样本比较的Wilcoxon检验与Kolmogorov-Smirnov(K-S)检验的功效进行比较。方法采用Matlab7.5软件编程,利用MonteCarlo方法模拟不同总体条件下两种方法的检验功效。结果对正态分布,两总体方差比率越大K-S检验的功效越高,而Wilcoxon检验则受方差比率的影响不大;对偏态分布,两检验法在方差不等时功效更高。方差相等且样本量较大的两组数据比较时,Wilcoxon检验功效高于K-S检验;其余情况则K-S检验功效更高;如果样本量足够大,两种方法功效接近。结论当两组样本方差相等且样本量较大时(n≥50)建议采用Wilcoxon检验,而在其他条件下均可采用K-S检验,当效应量ES≥0.8且样本量n≥50时两种方法均可。

Objective To compare the power of the Wilcoxon Rank-Sum test and Kolmogorov-Smirnov（K-S） test on completely randomized design of independent samples.Methods Using MATLAB program,Monte Carlo method was used to compute the powers of the two tests of samples from different populations.Results Under normal distribution,the power of K-S test was higher with the increase of the variance ratio,but the variance ratio has little effect on Wilcoxon test.Under the skewed distribution,two tests held larger powers when the samples had unequal variance.For equal variance and large sample size,the power of Wilcoxon test was higher than that of K-S test;otherwise,the conclusion is contrary.With the increase of the sample size,the powers of two tests have no difference.Conclusion Wilcoxon test is appropriate to the samples with equal variance and large sample size（n≥50）;else K-S test could be selected.When effect size is large（ES≥0.8） and sample size is large enough（n≥50）,two tests are both recommended.