Briefly, Kendall's tau-a is the difference between the probability of
concordance and discordance, where "concordance" is the event that the
larger of 2 X-values is associated with the larger of the 2
corresponding Y-values, and discordance is the event that the larger
X-value is associated with the smaller Y-value. Somers' D of Y with
respect to X, denoted D_YX, is the difference between the 2
corresponding CONDITIONAL probabilities, assuming that the 2 X-values
are ordered (instead of being tied). And Kendall's tau-b is the quantity
taub_XY = sign(taua_XY) * sqrt(D_XY * D_YX)
or (in other words) the common sign of D_XY and D_YX multiplied by the
geometric mean of their 2 absolute values.
I personally am more keen on having confidence intervals for Somers' D
and Kendall's tau-a because they can be interpreted in words as
differences between probabilities, which you cannot do with Kendall's
tau-b. There are a large number of downloadable articles,
pre-publication drafts and presentations on my website (see my signature
below) about the "Kendall family" of rank parameters, which are all
defined in terms of Kendall's tau-a and also include median slopes,
differences and ratios.
I hope this helps.
Best wishes
Roger
Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: [email protected]
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Joseph
Coveney
Sent: 06 December 2006 05:18
To: Statalist
Subject: Re: st: probability and z-statistic
Deidra Young wrote:
Hi Roger,
Only one thing I don't quite follow...
The tab command will produce Kendall's tau-b and approximate SE.
However,
Sommers' D produces tau-a only.
How do tau-a and tau-b differ?
------------------------------------------------------------------------
--------
You'll find a description of each on Roger's website. Take a look at
Section 2 on Page 2 of
www.imperial.ac.uk/nhli/r.newson/papers/params.pdf
Joseph Coveney
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
