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
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