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st: Re: reliability with ordinal data-Kendall's w?


From   "Joseph Coveney" <jcoveney@bigplanet.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: reliability with ordinal data-Kendall's w?
Date   Tue, 14 Dec 2010 09:03:36 +0900

Robert Ploutz-Snyder wrote:

I use Somers' d in other instances, but thought it not clear that it is
appropriate for reliability analysis?  

I arrive at this as:  In the case with two continuously scaled variables (A,B)
we use Pearson's r to describe the association (correlation), however if we are
really talking about the SAME thing measured with two devices or by two raters
(Y1,Y2) we would rely on ICC or Kappa statistics to understand reliability.  

Perhaps I am being over simplistic, but in my view, Somers' d would be an
appropriate tool for the first situation above (A,B), but perhaps not the second
(Y1,Y2).

My second reason is that Somers' d is closely related to Kendall's tau a, except
again how they handle ties.  But Kendall also developed the W statistic for use
in reliability analysis.  But that's where my knowledge of Kendall's W ends--I
do not have a good reference book on the shelf to tap so I don't really know how
W differes from tau... and where d fits into the mix.

--------------------------------------------------------------------------------

Richard Goldstein's -friedman- will compute Kendall's W (coefficient of
concordance).  -findit friedman- will show more about it.

Interpreting kappa is problematic because of its dependence on prevalence (see,
for example, http://nicolaorsini.altervista.org/stata/tutorial/k/tu_kapprevi.htm
).  In your case, kappa interpretation is even more problematic because of the
need to use an arbitrary weighting scheme to accommodate the ordered categorical
data.

You can compute ICCs for ordered categorical data using -gllamm-.

Roger Newson has written about the Somers d and its relation to other
nonparametric statistics. -findit somersd- will show user group presentations
and white papers that he's made available for downloading.

Joseph Coveney


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