I have a set of independent null hypothesis significance tests and their resulting p-values and I would like to make the claim that they are not all null by looking at the distribution of independent p-values. Since under the (meta) null hypothesis that all my hypotheses are actually null, the distribution of p-values is uniform, I though that I could simply perform a Kolmogorov-Smirnov test on that distribution and report the resulting p-value. Is this legitimate and is this something that any of you has seen done before? If so, would you have a reference?
I know of false discovery rate by Storey and Tibshirani but I would really wish to have a single p-value for the whole distribution rather than a set of q-values.