To permute or not to permute
To permute or not to permute
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DOI：
10.1093/bioinformatics/btl383
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发表时间：
2006-09-15
期刊：
影响因子：
5.8
通讯作者：
Hsu, Jason C.
中科院分区：
文献类型：
--
作者：
Huang, Yifan;Xu, Haiyan;Hsu, Jason C.
当检验统计量的分布未知时，排列检验是检验无效假设的一种常用方法。为了检验两个均值的相等性，排列检验可能使用一个检验统计量，该统计量是单变量情况下两个样本均值的差。在多变量的情况下，它可能使用一个检验统计量，它是单变量检验统计量的最大值。置换检验则通过置换两个样本之间的观测值来估计检验统计量的零分布。我们将证明，对于这样的检验，如果两个分布不相同（例如，当它们具有不等的方差，相关性或偏度时），则基于样本均值差的均值相等的置换检验即使在均值相等时也可能具有膨胀的I型错误率。我们的结果说明排列检验应该仅限于检验不同的分布。
Permutation test is a popular technique for testing a hypothesis of no effect, when the distribution of the test statistic is unknown. To test the equality of two means, a permutation test might use a test statistic which is the difference of the two sample means in the univariate case. In the multivariate case, it might use a test statistic which is the maximum of the univariate test statistics. A permutation test then estimates the null distribution of the test statistic by permuting the observations between the two samples.We will show that, for such tests, if the two distributions are not identical (as for example when they have unequal variances, correlations or skewness), then a permutation test for equality of means based on difference of sample means can have an inflated Type I error rate even when the means are equal. Our results illustrate permutation testing should be confined to testing for non-identical distributions.