>"You haven't shown anything where a true null hypothesis uniformly generates p-values between 0 and 1." Try this in R. It calculates p-values for testing the

>"You haven't shown anything where a true null hypothesis uniformly generates p-values between 0 and 1." Try this in R. It calculates p-values for testing the hypothesis that two groups (n=10) come from the same distribution (normal with mean=0, sd=1). It does 100,000 such comparisons, then makes a histogram. This results in approximately a uniform(0,1) distribution of p-values: hist(replicate(10^5,t.test(rnorm(10),rnorm(10),var.equal=T)$p.value)) If you increase to 10^6, 10^7, etc it will converge upon the uniform distribution. That is what people mean. Edit: Or something like this. Keep adding to the sample, the p-value will random walk between 0 and 1. The mean will converge onto 0.5: n=10; Nsim=10000 a=rnorm(n); b=rnorm(n) p=matrix(nrow=Nsim,ncol=2) for(i in 1:Nsim){ p[i,1]=length(a) p[i,2]=t.test(a,b,var.equal=T)$p.value a=c(a,rnorm(n)); b=c(b,rnorm(n)) plot(p[,1],p[,2],ylim=c(0,1), ylab="pvalue", xlab="sample size") }