From: Ruben Roa <RRoa_at_fisheries.gov.fk>

Date: Thu 10 Nov 2005 - 23:24:17 EST

Hi:

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

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Nov 11 00:35:00 2005

Date: Thu 10 Nov 2005 - 23:24:17 EST

> -----Original Message-----

*> From: r-help-bounces@stat.math.ethz.ch [SMTP:r-help-bounces@stat.math.ethz.ch] On Behalf Of Adaikalavan Ramasamy
**> Sent: Thursday, November 10, 2005 10:31 AM
**> To: Duncan Murdoch
**> Cc: r-help@stat.math.ethz.ch
**> Subject: Re: [R] How to find statistics like that.
**>
**> If my usage is wrong please correct me. Thank you.
**>
**> Here are my reason :
**>
**> 1. p-value is a (cumulative) probability and always ranges from 0 to 1.
**> A test statistic depending on its definition can wider range of possible
**> values.
**>
**> 2. A test statistics is one that is calculated from the data without the
**> need of assuming a null distribution. Whereas to calculate p-values, you
**> need to assume a null distribution or estimate it empirically using
**> permutation techniques.
**>
**> 3. The directionality of a test statistics may be ignored. For example a
**> t-statistics of -5 and 5 are equally interesting in a two-sided testing.
**> But the smaller the p-value, more evidence against the null hypothesis.
**>
**> Regards, Adai
**>
*

Hi:

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

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Nov 11 00:35:00 2005

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