Uniformity of Offsprings from Uniform and Non-Uniform Parents

Combining independent tests using reported p-values, which under Ho are observations from a standard uniform random variable, is usually done in meta-analysis using either the distributional theory of order statistics from the uniform distribution, or using -2 Sigma(n)(k=1) ln P-k (sic) chi(2)(2n), or alternatively combining the normal scores z(k) := Phi(-1)(p(k)). However the number of p-values available is in general very small, and it would seem reasonable to generate extra "pseudo-p-values" in order to improve power, exploiting the rich theory of order statistics and spacings of uniform and e,exponential samples. Publication bias, an important concern in meta-analytical syntheses, is also discussed, namely the extra difficulty of considering the sample of available p-values as upper-censored. As publication bias favours reporting of moderate p-values (tipicaly smaller than 0.05), we investigate the proportion of "combined" rejections of uniformity when the primary set of p-values copies in fact from an alternative parent popalations which has higher probability than a uniform parent of generating small values. We present evidence that this fake augmentation of samples doesn't in fact improve results.