R help - Nov 2012 - Compraring two independent samples

Hi,

In my reading of pairing means of two independent samples, I read statements
such as the standard error of the meanof X1 minus the mean of X2 is the
square root of s1^2/n1+s2^2/n2. Then I read:

"We could now derive the two independent samples confidence interval and
test statistic. However, a problem arises in that the distribution of the
test statistic (under the null hypothesis) will not be a t-distribution."

I keep seeing this type of thing stated in a variety of readings but I never
seem to get an explanation. This is just stated and the author goes on to an
alternate approach.

So, I am wondering if there is some sort of R simulation that could be used
to demonstrate that this distribution is not a t-distribution.

David



--
View this message in context:
http://r.789695.n4.nabble.com/Compraring-two-independent-samples-tp4649636.html
Sent from the R help mailing list archive at Nabble.com.

On 2012-11-15 10:17, David Arnold wrote:
> Hi,
>
> In my reading of pairing means of two independent samples, I read
statements
> such as the standard error of the meanof X1 minus the mean of X2 is the
> square root of s1^2/n1+s2^2/n2. Then I read:
>
> "We could now derive the two independent samples confidence interval
and
> test statistic. However, a problem arises in that the distribution of the
> test statistic (under the null hypothesis) will not be a
t-distribution."
>
> I keep seeing this type of thing stated in a variety of readings but I
never
> seem to get an explanation. This is just stated and the author goes on to
an
> alternate approach.
>
> So, I am wondering if there is some sort of R simulation that could be used
> to demonstrate that this distribution is not a t-distribution.
>
> David
If the populations are Normal, see Wikipedia (or elsewhere) for the
"Behrens?Fisher problem". If the populations are not Normal, I
don't
see why a t-distribution would be expected.

I seem to recall that Welch included some simulation results in his
Biometrika paper (1947? 1953?; I'm getting senile). Shouldn't be
difficult to generate in R. Maybe Greg Snow's TeachingDemos package
has something.

Peter Ehlers
>
>
>
> --
> View this message in context:
http://r.789695.n4.nabble.com/Compraring-two-independent-samples-tp4649636.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> 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.
>