5 Application to real data We examine the co-dependence between pairs of genes on chromosome 1 in the yeast gene expression dataset from Hughes et al. (2000), which contained N = 300 expres- sion levels. After removing genes with missing values, we had 94 genes and a family of ( 94 2 ) = 4371 pairs to examine simultaneously. Each pair was tested for independence by the tests of Spearman, Hoeffding, MIC, dCov and HHG on ranks, as well as by our new tests with m ranging from 2 to m$_{max}$ = 17. The null tables were based on 20000 permutations for N = 300. The adjusted p -values from the Benjamini–Hochberg procedure (Benjamini and Hochberg, 1995) were computed for each test statistic. Table 4 shows the pairwise agreements between the Benjamini–Hochberg procedure at level 0 . 05 using the different test statistics considered in each row, with the mini- mum p -value statistic based on DDP. Clearly, a large number of pairwise associations are missed when testing is performed with Spearman’s ρ compared to the minimum p -value statistic, and only a small number of gene pairs detected with Spearman are missed by the minimum p -value statistic (row 1 in Table 4). These findings contra- dict an earlier examination of the data. Steuer et al. (2002) concluded that the most widely used approach for pairwise association testing, namely Spearman correlation, performs equivalently to a mutual information based testing approach. The authors speculated that actual dependencies, if any, are linear. The number of discoveries using MIC, Hoeffding, and dCov are much smaller than using the minimum p -value statistic. HHG on ranks also discovers less co-dependencies compared with the min- imum p -value statistic. The agreement between the tests based on DDP and ADP was very high, as seen in the last row of Table 4 and in Figure 6, which shows the number of rejections for S DDP m × m and S ADP m × m for m = 2 , . . . , 17. We conclude that in this dataset there are many nonlinear associations, but powerful tests are necessary in order to detect such associations in light of the large number of simultaneous tests 37