How to compute p-Values

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