  We present the expected values from p-value hacking as a choice of the
minimum p-value among $m$ independents tests, which can be considerably lower
than the "true" p-value, even with a single trial, owing to the extreme
skewness of the meta-distribution.
  We first present an exact probability distribution (meta-distribution) for
p-values across ensembles of statistically identical phenomena. We derive the
distribution for small samples $2<n \leq n^*\approx 30$ as well as the limiting
one as the sample size $n$ becomes large. We also look at the properties of the
"power" of a test through the distribution of its inverse for a given p-value
and parametrization.
  The formulas allow the investigation of the stability of the reproduction of
results and "p-hacking" and other aspects of meta-analysis.
  P-values are shown to be extremely skewed and volatile, regardless of the
sample size $n$, and vary greatly across repetitions of exactly same protocols
under identical stochastic copies of the phenomenon; such volatility makes the
minimum $p$ value diverge significantly from the "true" one. Setting the power
is shown to offer little remedy unless sample size is increased markedly or the
p-value is lowered by at least one order of magnitude.

Applications;Statistical Finance