On Jan 14, 2009, at 4:27 PM, Andreas Klein wrote:
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:
You should realize that you are conflating p-values and Neyman-Pearson
hypothesis-testing formalism. It's perfectly possible that your
textbook is also doing the same sort of conflation.
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.
That does not sound correct. For one thing, no mention is made of
comparing the mean of a particular sample (of the same size as the
bootstrap samples) against the distribution of bootstrap means. For
another thing, you want to know if the sample mean either is less than
the 0.025 quantile of the boot_mean distribution or is greater than
the 0.975 quantile. Perhaps your informant meant to construct the test
as 2* min( sum(mean_boot[i] < mean_x)/1000, sum(mean_boot[i] > mean_x)/
1000).
In the HA: mean_x <0 directed one sided case, you are only interested
in whether the mean is below the 0.05 quantile. For the HA: mean_x >0
you want to know if mean_x is above the 0.95 quantile
In my realization of the mean_boot I get:
quantile(mean_boot, probs = c(0.025, 0.05, 0.95, 0.975) )
2.5% 5% 95% 97.5%
-0.2057778 -0.1643545 0.1562328 0.1825198
Those are going to be your critical points for alpha=0.05 Neyman-
Pearson tests of the sorts 1 and 2. The outer numbers are for the two-
sided alternative.
For calculation of the p-values, I still think you need ecdf and
probably Hmisc:::inverseFuntion as well. For p-values you need to go
from the observed value back to the proportion that exceed that value.
Regards,
Andreas.
--- David Winsemius <dwinsem...@comcast.net> schrieb am Mi, 14.1.2009:
Von: David Winsemius <dwinsem...@comcast.net>
Betreff: Re: [R] How to compute p-Values
An: klein82...@yahoo.de
CC: "r help" <r-help@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.rolshau...@biologie.uni-freiburg.de> schrieb
am Mi, 14.1.2009:
Von: gregor rolshausen
<gregor.rolshau...@biologie.uni-freiburg.de>
Betreff: Re: [R] How to compute p-Values
An: "r help"
<r-help@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@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@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@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@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.
