# [R] How to find statistics like that.

Mike Miller mbmiller at taxa.epi.umn.edu
Thu Nov 10 15:32:03 CET 2005

```On Thu, 10 Nov 2005, Ruben Roa wrote:

> A statistic is any real-valued or vector-valued function whose
> domain includes the sample space of a random sample. The
> p-value is a real-valued function and its domain includes the
> sample space of a random sample. The p-value has a sampling
> distribution. The code below, found with Google ("sampling distribution
> of the p-value" "R command") shows the sampling
> distribution of the p-value for a t-test of a mean when the null hypothesis
> is true.
> Ruben
>
> n<-18
> mu<-40
> pop.var<-100
> n.draw<-200
> alpha<-0.05
> draws<-matrix(rnorm(n.draw * n, mu, sqrt(pop.var)), n)
> get.p.value<-function(x) t.test(x, mu = mu)\$p.value
> pvalues<-apply(draws, 2, get.p.value)
> hist(pvalues)
> sum(pvalues <= alpha)
> [1] 6

The sampling distribution of a p-value when the null hypothesis is true
can be given more simply by this R code:

runif()

That holds for any valid test, not just a t test, that produces p-values
distributed continuously on [0,1].  Discrete distributions can't quite do
that without special tweaking.

Mike

```