Uniformity of offsprings from uniform and non-uniform parents

Combining independent tests using reported p-values, which under H
₀
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 -2Sigma
_k=1

ⁿ
ln P
_k
capchi
_2n

²
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 ldquopseudo-p-valuesrdquo in order to improve power, exploiting the rich theory of order statistics and spacings of uniform and 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 (typically smaller than 0.05), we investigate the proportion of ldquocombinedrdquo rejections of uniformity when the primary set of p-values comes in fact from an alternative parent populations 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.