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From |
Steven Samuels <[email protected]> |

To |
[email protected] |

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

Date |
Tue, 14 Dec 2010 12:09:34 -0500 |

Steve [email protected] On Dec 14, 2010, at 10:16 AM, Nick Cox wrote:

Nick [email protected] Airey, David C

Nick Cox

In this kind of territory, I would always1. Check out what is said in Rupert G. Miller, Beyond ANOVA. See onthe CRC Press reissue< http://www.crcpress.com/utility_search/search_results.jsf?conversationId=250169Your library may hold a copy of the Wiley original.2. Be wary of the stark cookbooky alternative: data if normal, ranksotherwise. What happened to the idea of transformations or linkfunctions? How do you decide when the data are approximately normalany way?Here is an example of a different approach. In the auto data, -mpg-given -foreign- is neither normal nor heteroscedastic. But these aresecondary 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 -3.80The change of sign of what -glm- calls the z statistic is anexpected side-effect of changing to inverse transformations. Moreimportantly, z changes only very slowly and the collective set ofresults points to the idea that 1/mpg is a more appropriate scalethan mpg on which to test for differences. This of course matchesbasic science.Generalized linear models are nearly 40 years old as a family. Whenare they going to receive the recognition they deserve?

Airey, David C

I was reading a little about what to do when you have both unequalvariance and non-normality. Neither the equal variance t-test northe Mann-Whitney U test are best when you want to interpret thedifference in means or medians.I had found the Stata command -fprank-, but it turns out thisrobust ranks test doesn't escape a symmetry assumption to interpretthe 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 ofthe Student's t test and the Welch t' test for non-normalpopulations with unequal variances. Canadian Journal ofExperimental Psychology 47:3, 523-539).This appears easy and satisfying solution to teach with: always useunequal variances t-test and use ranks if the data are also notnormal.

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

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

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