The -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 p-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 L-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 L(1) 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 L(1)-distance test statistic. The performance and power of the L(1)-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 L(1)-distance test appears to be nearly as powerful as its L(2) counterpart. The lower computational intensity of the L(1)-distance test allows computation of exact quantiles of the null distribution for larger sample sizes than is possible for the Cramér-von Mises test.