If the size factors are not equal across samples, but not correlated with condition, conditioning on the mean of normalized counts should also provide uniformly distributed p as with conditioning on the mean of counts, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\bar {K}_{i}$ \end{document}K¯i. We may consider a pathological case where the size factors are perfectly confounded with condition, in which case, even under the null hypothesis, genes with low mean count would have non-uniform distribution of p, as one condition could have positive counts and the other condition often zero counts. This could lead to non-uniformity of p under the null hypothesis; however, such a pathological case would pose problems for many statistical tests of differences in mean.
