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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: When is the t-test appropriate? |

Date |
Thu, 29 Aug 2002 20:06:25 +0100 |

Jon Wainwright > I would like to compare the means of two very small random > samples (n1=3, > n2=7). Both samples were drawn from populations of unknown > distribution. Is > Stata's ttest appropriate in such a situation, or does it > require the > underlying populations to be normally distributed? If ttest is not > appropriate, can anyone suggest are more appropriate method > for testing the > difference of the means? Lots of answers are possible on different levels. Whatever one says in one sense is likely to be wrong in another, but here's my take: 1. Supposedly, the t test takes account of your sample sizes. It is possible that your data are such that the answer is clearcut even with very small sizes, but perhaps more likely is that you will fail to get a significant result (at conventional levels). A common but not universal interpretation of that would be that it indicates not so much that there is no difference, but more that the sample sizes are not large enough to indicate it reliably. Some would say that this is the main (or even only) role of a significance test. 2. At the same time, there is a underlying assumption of normality, whatever the sample size. Nevertheless, there are many theoretical results, much practical experience and a lot of folklore to suggest that moderate non-normality may not be a problem. (Naturally, what is "moderate"?) In addition, other assumptions such as equal variances and independence may be much more critical. For an outstanding discussion with much more precision, see Rupert G. Miller's "Beyond ANOVA". 3. Calculate confidence intervals and look at them graphically. There are various possible warning signs, for example if one confidence limit is an unattainable value (e.g. physically, biologically, economically impossible) then you have an enigma wrapped inside a riddle within a mystery, or whatever it was that Winston Churchill said on a totally different topic. 4. Bootstrap! 5. As Ricardo Ovaldia suggested, you could try a different approach, such as Mann-Whitney. That, however, tests a different hypothesis and says nothing directly about means. 6. Show us the data. Nick n.j.cox@durham.ac.uk * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: When is the t-test appropriate?***From:*Jon Wainwright <jwainwright@austin.rr.com>

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