> -----Original Message----- > From: Mike Miller [SMTP:[EMAIL PROTECTED] > Sent: Thursday, November 10, 2005 12:32 PM > To: Ruben Roa > Cc: [EMAIL PROTECTED]; Duncan Murdoch; r-help@stat.math.ethz.ch > Subject: Re: [R] How to find statistics like that. > > 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 > ------------ Theorem 2.1.4 in Casella and Berger (1990, p. 52). Ruben
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