Figure 5.

Estimates of the null p-value quartiles vary as a function of signal intensity for four common two sample test procedures applied to the re-loessed dataset 10a. The x-axes correspond to the rankit (i.e., $\frac{\text{rank of value}}{\text{total}\#\text{of values}+1}$) of the log of the product of the expression means. The y-axes correspond the observed two-sided p-values. Solid and dashed grey lines indicate the theoretical medians and quartiles, respectively. The null p-values were modeled as a function of a 4^th order polynomial for rankit intensity. Red lines correspond to the quantile regression fits for τ = 0.5 (solid) and τ = 0.25, 0.75 (dashed). (a) P-values for the two sample t-test conducted under the assumption of equal variances. (b) P-values for the two sample t-test conducted under the assumption of unequal variances (a.k.a. Welch's test). Relaxing the assumption of equal variances provides for only a slight improvement in the distribution of the null p-values (c) P-values for the Wilcoxon Rank Sum test. (d) P-values for the permutation test [19,20]. Permutation based approaches are not robust to the systematic errors manifest in the Stage II data matrix.