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.
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/faqs/resources/statalist-faq/
* http://www.ats.ucla.edu/stat/stata/
