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Re: st: RE: RE: median equality test for non normal variables


From   Ronan Conroy <rconroy@rcsi.ie>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE: RE: median equality test for non normal variables
Date   Tue, 25 May 2010 11:06:15 +0100

<..>

There is an interesting question concerning the difference between what people think they are doing when applying a 'nonparametric' test and what is actually happening.

Consider the following data:

input var group
1 0
2 0
3 0
4 0
4 0
4 0
4 0
4 1
4 1
4 1
4 1
5 1
6 1
7 1
end

Note that the median coincides with the highest value in group zero and the lowest value in group 1.

What we get now depends critically on what we ask for:

Test for equality of medians using -qreg- : P=1.000 (the medians are the same)
Wilcoxon rank sum test : Prob > |z| =   0.0196
Median test (which does not test for equality of medians, NB) : Pearson chi2(1) = 3.8182 Pr = 0.051 Median test, continuity corrected : Pearson chi2(1) = 1.6970 Pr = 0.193
Ordered logit regression with group as a predictor : P =  0.997
'Harrell's C' (as calculated by -somersd-) : .76, P < 0.001


I have put quotes around Harrell's C, as this quantity is simply a rescaling of Mann Whitney's U, dividing it by its maximum possible value, and was first proposed by Richard Herrnstein in 1976 (Herrnstein, R. J., Loveland, D. H., & Cable, C. (1976). Natural concepts in pigeons. Journal of Experimental Psychology: Animal Behavior Processes, 2, 285–302), who termed it rho. Fans of terminological chaos will also recognise the entity as the area under the ROC curve. Harrell's C is identical with rho only when the data are uncensored (James A. Koziol, Zhenyu Jia.T he Concordance Index C and the Mann-Whitney Parameter Pr(X>Y) with Randomly Censored Data Biometrical Journal 2009:51(3);467 - 474.)

I fancy that there is an amusing paper on this, clarifying the hypotheses being tested in each case, if anyone has time to write one...

I am looking again at the t-test, which, after a couple of Kolmogorov- Smirnovs, is beginning to look more and more attractive.


Ronan Conroy
=================================

rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
Beaux Lane House, Dublin 2, Ireland
+353 (0)1 402 2431
+353 (0)87 799 97 95
+353 (0)1 402 2764 (Fax - remember them?)
http://rcsi.academia.edu/RonanConroy

P    Before printing, think about the environment





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