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. 2006 Sep 14;2006(1):85769. doi: 10.1155/BSB/2006/85769

The Inline graphic-Version of the Cramér-von Mises Test for Two-Sample Comparisons in Microarray Data Analysis

Yuanhui Xiao 1,2,✉, Alexander Gordon 1,3, Andrei Yakovlev 1
PMCID: PMC3171322  PMID: 18427586

Abstract

Distribution-free statistical tests offer clear advantages in situations where the exact unadjusted Inline graphic-values are required as input for multiple testing procedures. Such situations prevail when testing for differential expression of genes in microarray studies. The Cramér-von Mises two-sample test, based on a certain Inline graphic-distance between two empirical distribution functions, is a distribution-free test that has proven itself as a good choice. A numerical algorithm is available for computing quantiles of the sampling distribution of the Cramér-von Mises test statistic in finite samples. However, the computation is very time- and space-consuming. An Inline graphic counterpart of the Cramér-von Mises test represents an appealing alternative. In this work, we present an efficient algorithm for computing exact quantiles of the Inline graphic-distance test statistic. The performance and power of the Inline graphic-distance test are compared with those of the Cramér-von Mises and two other classical tests, using both simulated data and a large set of microarray data on childhood leukemia. The Inline graphic-distance test appears to be nearly as powerful as its Inline graphic counterpart. The lower computational intensity of the Inline graphic-distance test allows computation of exact quantiles of the null distribution for larger sample sizes than is possible for the Cramér-von Mises test.

[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]

Contributor Information

Yuanhui Xiao, Email: yxiao@bst.rochester.edu.

Alexander Gordon, Email: alexander_gordon@urmc.rochester.edu.

Andrei Yakovlev, Email: andrei_yakovlev@urmc.rochester.edu.

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