Thank you Roger!
Deidra
On 6/12/06 9:04 PM, "Newson, Roger B" <[email protected]>
> 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/
>
*
* 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/
