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Re: st: Optimal ratio of sample sizes in two sample t test


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Optimal ratio of sample sizes in two sample t test
Date   Mon, 7 Jan 2013 16:09:18 -0500

On Mon, Jan 7, 2013 at 2:50 PM, Douglas McKee <douglas.mckee@yale.edu> wrote:

<<<Suppose I'm trying to choose the sample sizes for a study where I
have two populations that are equally costly to sample.  If I know the
standard deviations of each group, I can use sampsi to compute the n's
when I specify effect size, alpha and desired power.  But suppose one
sample has a low variance and the other has a high variance.  Doesn't
this mean I should sample more from the high variance group?  Is there
a way to make Stata tell me the optimal n1/n2 ratio?  Or should I
write a wrapper around sampsi that tries a variety of ratios and tells
me which one yields the smallest n1+n2?>>>

I don't see this as being an easy problem to solve as the decision
rule with clearly unequal variances is one of the whack-a-mole
problems in statistics:

http://en.wikipedia.org/wiki/Behrens_Fisher_problem

How different are the standard deviations? If the ratio isn't too far
from 2:1, then you probably are OK doing near-equal sample size, but
of course you could optimize the MSE, which would lean towards the
population with smaller variance.

Differences in SD may be the sign of a larger issue, though. Are the
variables better analyzed on a different scale? So for instance, maybe
it would be better to use a generalized linear model to accommodate
linearity inside a log link.
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