# P-values distribution meaning

Could anyone tell me what changes in the p-value distribution mean?

I mean, for example, what does mean that the p-values follow a uniform distribution? and what happens if the p-values distribution has many p-values between 0 and 0.05 and then it flattens out?

hope this helps

"To clarify a bit. The p-value is uniformly distributed when the null hypothesis is true and all other assumptions are met. The reason for this is really the definition of alpha as the probability of a type I error. We want the probability of rejecting a true null hypothesis to be alpha, we reject when the observed p-value<α, the only way this happens for any value of alpha is when the p-value comes from a uniform distribution. The whole point of using the correct distribution (normal, t, f, chisq, etc.) is to tranform from the test statistic to a uniform p-value. If the null hypothesis is false then the distribution of the p-value will (hopefully) be more weighted towards 0.

The Pvalue.norm.sim and Pvalue.binom.sim functions in the TeachingDemos package for R will simulate several data sets, compute the p-values and plot them to demonstrate this idea.

Also see:

Murdoch, D, Tsai, Y, and Adcock, J (2008). P-Values are Random Variables. The American Statistician, 62, 242-245.

for some more details."

• And if the distributions of p-values does not follow anything (it is not uniform nor with many p-values between 0 and 0.05), what does it mean? – Peter Pfand Sep 13 '14 at 8:44