[R] How to compute p-Values

[Andreas Klein]

Ok... I set up the problem by some code as requested:

Example:

x <- rnorm(100)

mean_x <- mean(x)

mean_boot <- numeric(1000)

for (i in 1:1000) {

  mean_boot[i] <- mean(sample(x,100,replace=TRUE))

}


How can I compute the p-Value out of mean_boot for the following tests:

1. H0: mean_x = 0 vs. H1: mean_x != 0

2. H0: mean_x >= 0 vs. H1: mean_x < 0



Is there a possibility to construct such p-Values or did I get something wrong?

Someone told, that the p-Value = 2 * min(sum(mean_boot>=0)/1000, sum(mean_boot<0)/1000) for the first (two sided) test is, but didn't get the idea behind it. Maybe someone can explain it, if it is the solution to the problem.

Regards,
Andreas.



--- David Winsemius <dwinsemius at comcast.net> schrieb am Mi, 14.1.2009:

> Von: David Winsemius <dwinsemius at comcast.net>
> Betreff: Re: [R] How to compute p-Values
> An: klein82517 at yahoo.de
> CC: "r help" <r-help at r-project.org>
> Datum: Mittwoch, 14. Januar 2009, 16:40
> I think we are at the stage where it is your responsibility
> to provide some code to set up the problem.
> 
> --David Winsemius
> On Jan 14, 2009, at 9:23 AM, Andreas Klein wrote:
> 
> > Hello.
> > 
> > What I wanted was:
> > 
> > I have a sample of 100 relizations of a random
> variable and I want a p-Value for the hypothesis, that the
> the mean of the sample equals zero (H0) or not (H1). That is
> for a two sampled test.
> > The same question holds for a one sided version, where
> I want to know if the mean is bigger than zero (H0) or
> smaller or equal than zero (H1).
> > 
> > Therfore I draw a bootstrap sample with replacement
> from the original sample and compute the mean of that
> bootstrap sample. I repeat this 1000 times and obtain 1000
> means.
> > 
> > Now: How can I compute the p-Value for an one sided
> and two sided test like described above?
> > 
> > 
> > 
> > Regards,
> > Andreas
> > 
> > 
> > --- gregor rolshausen
> <gregor.rolshausen at biologie.uni-freiburg.de> schrieb
> am Mi, 14.1.2009:
> > 
> >> Von: gregor rolshausen
> <gregor.rolshausen at biologie.uni-freiburg.de>
> >> Betreff: Re: [R] How to compute p-Values
> >> An: "r help"
> <r-help at r-project.org>
> >> Datum: Mittwoch, 14. Januar 2009, 11:31
> >> Andreas Klein wrote:
> >>> Hello.
> >>> 
> >>> 
> >>> How can I compute the Bootstrap p-Value for a
> one- and
> >> two sided test, when I have a bootstrap sample of
> a
> >> statistic of 1000 for example?
> >>> 
> >>> My hypothesis are for example:
> >>> 
> >>> 1. Two-Sided: H0: mean=0 vs. H1: mean!=0
> >>> 2. One Sided: H0: mean>=0 vs. H1: mean<0
> >>> 
> >>> 
> >> hi,
> >> do you want to test your original t.test against
> t.tests of
> >> bootstrapped samples from you data?
> >> 
> >> if so, you can just write a function creating a
> vector with
> >> the statistics (t) of the single t.tests (in your
> case 1000
> >> t.tests each with a bootstrapped sample of your
> original
> >> data -> 1000 simulated t-values).
> >> you extract them by:
> >> 
> >>> tvalue=t.test(a~factor)$statistic
> >> 
> >> then just calculate the proportion of t-values
> from you
> >> bootstrapped tests that are bigger than your
> original
> >> t-value.
> >> 
> >>>
> p=sum(simualted_tvalue>original_tvalue)/1000
> >> 
> >> 
> >> (or did I get the question wrong?)
> >> 
> >> cheers,
> >> gregor
> >> 
> >> ______________________________________________
> >> R-help at r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide
> >> http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained,
> >> reproducible code.
> > 
> > 
> > 
> > 
> > ______________________________________________
> > R-help at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained,
> reproducible code.