Suppose I have three (or more) samples, from three (or more) different
populations. According to my subject matter expert, he wants to estimate
a linear combination of the means, say for example
0.5*mu1 + 0.5*mu2 - mu3
where mu1, mu2 and mu3 are the population means. I know how to compute
this estimate, it is done by simply replacing the population means with
the sample means. If I assume the original populations are normal and
that the population variances are equal, I can compute the variance of
this linear combination. Pretty straightforward stuff.
However, I want to create a t-test to test the null hypothesis that this
linear combination of means is equal to zero, using an estimate of
variance derived from the data, rather than a population variance, which
is unknown. In doing so, I run into the mathematical difficulty that I
do not know the proper degrees of freedom for this test. (And yes, I
know that for the special case of estimating mu1 - mu2 there are
textbook formulas for this t-test, however I really am interested in
linear combinations of more than two means).
I feel like I am missing something very obvious; however, if someone
knows, or can point me to the proper formula for a t-test on a linear
combination of means, it would be greatly appreciated.
--
Paige Miller
[EMAIL PROTECTED]
http://www.kodak.com
"It's nothing until I call it!" -- Bill Klem, NL Umpire
"When you get the choice to sit it out or dance, I hope you dance" --
Lee Ann Womack
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
