Assessment of P-value variability in the current replicability crisis
  Increased availability of data and accessibility of computational tools in recent years have created unprecedented opportunities for scientific research driven by statistical analysis. Inherent limitations of statistics impose constrains on reliability of conclusions drawn from data but misuse of statistical methods is a growing concern. Significance, hypothesis testing and the accompanying P-values are being scrutinized as representing most widely applied and abused practices. One line of critique is that P-values are inherently unfit to fulfill their ostensible role as measures of scientific hypothesis's credibility. It has also been suggested that while P-values may have their role as summary measures of effect, researchers underappreciate the degree of randomness in the P-value. High variability of P-values would suggest that having obtained a small P-value in one study, one is, nevertheless, likely to obtain a much larger P-value in a similarly powered replication study. Thus, "replicability of P-value" is itself questionable. To characterize P-value variability one can use prediction intervals whose endpoints reflect the likely spread of P-values that could have been obtained by a replication study. Unfortunately, the intervals currently in use, the P-intervals, are based on unrealistic implicit assumptions. Namely, P-intervals are constructed with the assumptions that imply substantial chances of encountering large values of effect size in an observational study, which leads to bias. As an alternative to P-intervals, we develop a method that gives researchers flexibility by providing them with the means to control these assumptions. Unlike endpoints of P-intervals, endpoints of our intervals are directly interpreted as probabilistic bounds for replication P-values and are resistant to selection bias contingent upon approximate prior knowledge of the effect size distribution. 
Olga A. Vsevolozhskaya, Gabriel Ruiz, Dmitri V. Zaykin
q-bio.GN stat.ME