The [Image: see text]-Version of the Cramér-von Mises Test for Two-Sample Comparisons in Microarray Data Analysis

Distribution-free statistical tests offer clear advantages in situations where the exact unadjusted [Image: see text]-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 [Image: see text]-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 [Image: see text] 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 [Image: see text]-distance test statistic. The performance and power of the [Image: see text]-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 [Image: see text]-distance test appears to be nearly as powerful as its [Image: see text] counterpart. The lower computational intensity of the [Image: see text]-distance test allows computation of exact quantiles of the null distribution for larger sample sizes than is possible for the Cramér-von Mises test.