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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. * * 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/

**Follow-Ups**:**RE: st: Optimal ratio of sample sizes in two sample t test***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**References**:**st: Optimal ratio of sample sizes in two sample t test***From:*Douglas McKee <douglas.mckee@yale.edu>

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