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From |
Nick Cox <[email protected]> |

To |
"'[email protected]'" <[email protected]> |

Subject |
st: RE: RE: two sample test under generalized Behrens-Fisher conditions |

Date |
Tue, 14 Dec 2010 15:16:34 +0000 |

I see the problem. I couldn't (wouldn't) fit -glm- in an introductory course either. In similar circumstances I usually assert that t tests work well even if the assumptions are not well satisfied. This is an idea that goes back at least to G.E.P. Box in Biometrika 1953: Box, G.E.P. 1953. Non-normality and tests on variances. Biometrika 40: 318-35. Nick [email protected] Airey, David C I was looking for "stark cookbooky" solutions for a (too) short intro course that will not address GLM. But transformations they will be told about, and the last time I taught this course, your help file about transformations was required reading. Thanks for that citation. Looks like a good book. Nick Cox > In this kind of territory, I would always > > 1. Check out what is said in Rupert G. Miller, Beyond ANOVA. See on the CRC Press reissue > < > http://www.crcpress.com/utility_search/search_results.jsf?conversationId=250169 > > > > Your library may hold a copy of the Wiley original. > > 2. Be wary of the stark cookbooky alternative: data if normal, ranks otherwise. What happened to the idea of transformations or link functions? How do you decide when the data are approximately normal any way? > > Here is an example of a different approach. In the auto data, -mpg- given -foreign- is neither normal nor heteroscedastic. But these are secondary issues. Consider this set of results. In each -family(normal)- is implied. > > foreach v in "power 1" "power 0.5" "log" "power -0.5" "power -1" { > qui glm mpg foreign, link(`v') > mat b = e(b) > mat V = e(V) > di "`v'" "{col 20}" %3.2f b[1,1] / sqrt(V[1,1]) > } > > power 1 3.63 > power 0.5 3.70 > log 3.75 > power -0.5 -3.78 > power -1 -3.80 > > The change of sign of what -glm- calls the z statistic is an expected side-effect of changing to inverse transformations. More importantly, z changes only very slowly and the collective set of results points to the idea that 1/mpg is a more appropriate scale than mpg on which to test for differences. This of course matches basic science. > > Generalized linear models are nearly 40 years old as a family. When are they going to receive the recognition they deserve? Airey, David C >> I was reading a little about what to do when you have both unequal variance and non-normality. Neither the equal variance t-test nor the Mann-Whitney U test are best when you want to interpret the difference in means or medians. >> >> I had found the Stata command -fprank-, but it turns out this robust ranks test doesn't escape a symmetry assumption to interpret the location difference. >> >> I found that some recommend using Welch's t-test on the ranked data (Zimmerman and Zumbo (1993) Rank transformations and the power of the Student's t test and the Welch t' test for non-normal populations with unequal variances. Canadian Journal of Experimental Psychology 47:3, 523-539). >> >> This appears easy and satisfying solution to teach with: always use unequal variances t-test and use ranks if the data are also not normal. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: RE: RE: two sample test under generalized Behrens-Fisher conditions***From:*"Lachenbruch, Peter" <[email protected]>

**Re: st: RE: RE: two sample test under generalized Behrens-Fisher conditions***From:*Steven Samuels <[email protected]>

**References**:**st: RE: two sample test under generalized Behrens-Fisher conditions***From:*"Airey, David C" <[email protected]>

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