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From |
"Newson, Roger B" <r.newson@imperial.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: significance test between two kendalls' tau coefficents ? |

Date |
Thu, 4 Dec 2008 14:11:43 -0000 |

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.htm Newson 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.html or download a pre-publication draft from http://www.imperial.ac.uk/nhli/r.newson/papers.htm Newson 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.html or download a pre-publication draft from http://www.imperial.ac.uk/nhli/r.newson/papers.htm Newson 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.htm Newson 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.html or download a pre-publication draft from http://www.imperial.ac.uk/nhli/r.newson/papers.htm Newson 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.html Roger 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: r.newson@imperial.ac.uk Web page: http://www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop genetics/reph/ Opinions expressed are those of the author, not of the institution. -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Marcus Fischer Sent: 04 December 2008 11:35 To: statalist@hsphsun2.harvard.edu 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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: RE: significance test between two kendalls' tau coefficents ?***From:*"Feiveson, Alan H. (JSC-SK311)" <Alan.H.Feiveson@nasa.gov>

**References**:**st: significance test between two kendalls' tau coefficents ?***From:*"Marcus Fischer" <Marcus.Fischer@klinik.uni-regensburg.de>

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