Assuming that p-values come from continuous phenotypes, the method used to calculate TATES p-values should, in theory, produce p-values that are distributed in a way that does not increase Type I error. In the ideal case the distribution will be uniform (Bland 2013; Murdoch et al. 2008). However, even in less than ideal cases, for all “good” statistics, the left side of probability distribution function (pdf) must be <= 1. Otherwise, the results will be inflated, corresponding to how much the pdf > 1. Since the construction of the TATES test corresponds to a continuous null hypothesis, in this case the p-value distribution should be uniform or at least not exceed 1 around 0. Violation of this assumption (i.e., observing inflation in p-values, as indicated by pdf > 1 around 0) would suggest that the TATES procedure produces an excess of Type I errors, potentially leading to inaccurate conclusions.
