[R] How to find statistics like that.

[Duncan Murdoch]

On 11/10/2005 9:32 AM, Mike Miller wrote:
> 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.

Nor can most composite null hypotheses, e.g.

H0: mu <= 0 versus H1: mu > 0

A t-test may be an appropriate test, but its p-value is not uniformly 
distributed when mu is -1, even though the null is true.

Duncan Murdoch