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Re: st: Friedman tests


From   Roger Newson <roger.newson@kcl.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Friedman tests
Date   Wed, 23 Mar 2005 13:17:21 +0000

At 10:32 23/03/2005, Ronan Conroy wrote:
Ashley Harris wrote:

Statalist,

What I have nonparametric data for 3 groups, 1 dependent variable (ratio)
and 2 independent variables (technique and analysis type).
Data are not parametric or nonparametric. And, indeed, the terms are confusing when applied to statistical procedures. I presume that you have a dependent variable that you can't put into a regression or anova. Nevertheless, before you head off an do a rank test, consider using some of the more powerful alternatives.

- counted data: consider negative binomial regression (or Poisson, if counts are of rare events)
- ordered categories: ordinal logistic regression springs to mind

With these techniques, you can explore multiple independent variables, just as you can in regression. Of course, these models have assumptions, just as any model does, and you should check that your data conform to these assumptions.

Rank tests tend to be an index of despair. They lose important information by losing the original measurement scale of the dependent variable. This allows you to assess statistical significance, but not real life importance.
However, rank methods can be used to produce confidence intervals, sometimes for median differences and/or median ratios on the scale of the original outcome (so you do not lose the original measurement scale after all). See, for instance, Newson (2002), which can be downloaded in preprint form by typing

findit params

in Stata.

Having said that, rank statistics are still subject to the limitations that you cannot use them to calculate confounder-adjusted effects of an exposure (except possibly by using propensity score methods, in which case you still need regression statistics to define the propensity score). And Ronan is entirely right to point out that there are no such things as "nonparametric data", and that it is confusing and misleading even to talk about "nonparametric statistical procedures".

I hope this helps.

Roger



References

Newson R. 2002. Parameters behind "nonparametric" statistics: Kendall's tau, Somers' D and median differences. The Stata Journal 2(1): 45-64.


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
Division of Asthma, Allergy and Lung Biology
King's College London

5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
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or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://phs.kcl.ac.uk/rogernewson/

Opinions expressed are those of the author, not the institution.

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