Yes, it is possible. However, how to do it depends on whether the

Kendall's tau coefficients are from the same sample, or from different

samples.

In Stata, confidence intervals for Kendall's tau-a statistics and their

differences can be calculated using the -somersd- package, downloadable

from SSC using the -ssc- command. This package is described in Newson

(2002), Newson (2006a) and Newson (2006b), and calculates confidence

intervals for a wide range of rank statistics, including some with

sample weighting, clustering and/or stratification.

Often, given a single outcome variable Y and 2 positive predictors X and

W, we want to know which of the 2 positive predictors predicts Y better.

This is because, as proved in Newson (2006a) and Newson (2002), if a

positive association of Y with X is caused by a positive association of

both variables with W, then we must have the inequalities

tau(Y,X) <= tau (W,X)

tau(X,Y) >= tau(W,Y)

where tau(.,.) is Kendall's tau-a. Typically, in Stata, we type

somersd Y X W, taua tdist

lincom X-W

The -somersd- command, with the -taua- option, calculates confidence

intervals for the Kendall's tau-a parameters tau(Y,X) and tau(Y,W). The

-lincom- command calculates a confidence interval for the difference

tau(Y,X)-tau(Y,W).

Sometimes, by contrast, we may want to estimate the difference between 2

tau(Y,X) statistics in different subpopulations, from which we have

taken 2 different subsamples. In this case, we can use the -somersd-

package with the -parmest- package, also downloadable from SSC. The

-parmest- package creates and processes output datasets (or resultssets)

with 1 observation per estimated parameter and data on estimates,

standard errors, confidence limits and P-values, and is described in

Newson (2003), Newson (2004), and Newson(2008). If the variable -subpop-

indicates which of 2 subpopulations an observation belongs to, then we

may type in Stata

parmby "somersd Y X, taua tdist", by(subpop) norestore

list

metaparm [iwei=(subpop==2)-(subpop==1)] if parm=="X", list(,)

The -parmby- command creates, in the memory, an output dataset (or

resultsset), with 1 observation per fitted tau-a parameter and data on

their estimates, standard errors, confidence limits, and P-values. (This

resultsset overwrites the original dataset.) The tau-a parameters, are

tau(Y,Y) in subpopulation 1, tau(Y,X) in subpopulation 1, tau(Y,Y) in

subpopulation 2, and tau(Y,X) in subpopulation 2. We want to compare the

2 tau(Y,X) parameters. (The tau(Y,Y) parameters are simply probabilities

that 2 randomly-chosen Y-values are unequal.) The list command lists all

the estimated parameters. The metaparm command calculates and lists a

confidence interval for the difference between the tau(Y,X) parameter in

subpopulation 2 and the tau(Y,X) parameter in subpopulation 1.

I hope this helps. Let me know if you have any queries.

Best wishes

Roger

References

Newson R. B. parmest and extensions. Presented at the 14th UK Stata User

Meeting, 8-9 September, 2008. Download presentation from

http://www.imperial.ac.uk/nhli/r.newson/usergp.htmNewson R. 2006b. Confidence intervals for rank statistics: Percentile

slopes, differences, and ratios. The Stata Journal 6(4): 497-520. Buy

the article from

http://www.stata-journal.com/archives.htmlor download a pre-publication draft from

http://www.imperial.ac.uk/nhli/r.newson/papers.htmNewson R. 2006a. Confidence intervals for rank statistics: Somers' D and

extensions. The Stata Journal 6(3): 309-334. Buy the article from

http://www.stata-journal.com/archives.htmlor download a pre-publication draft from

http://www.imperial.ac.uk/nhli/r.newson/papers.htmNewson R. From datasets to resultssets in Stata. Presented at the 10th

UK Stata User Meeting, 28-29 June, 2004. Download presentation and

handouts from

http://www.imperial.ac.uk/nhli/r.newson/usergp.htmNewson R. 2003. Confidence intervals and p-values for delivery to the

end user. The Stata Journal 3(3): 245-269. Download the article from

http://www.stata-journal.com/archives.htmlor download a pre-publication draft from

http://www.imperial.ac.uk/nhli/r.newson/papers.htmNewson R. 2002. Parameters behind "nonparametric" statistics: Kendall's

tau, Somers' D and median differences. The Stata Journal 2(1): 45-64.

Download the article from

http://www.stata-journal.com/archives.htmlRoger B Newson BSc MSc DPhil

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:

[hidden email]
Web page:

http://www.imperial.ac.uk/nhli/r.newson/Departmental Web page:

http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

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

-----Original Message-----

From:

[hidden email]
[mailto:

[hidden email]] On Behalf Of Marcus

Fischer

Sent: 04 December 2008 11:35

To:

[hidden email]
Subject: st: significance test between two kendalls' tau coefficents ?

I would like to compare two Kenadalls' tau coefficients. Is it possible

to test whether one coefficient is significantly higher than the other

one ?

Thanks.

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