Mike has raised an important issue here, because a "significant" difference between 2 Kendall's taus seems to imply that at least one of them is non-zero. A possible response is to use the hyperbolic arctangent transformation (also known as Fisher's z transformation), recommended by Edwardes (1995), as a Normalizing and variance-stabilizing transformation. This transformation is available in Stata by using the -somersd- package with the -transf(z)- option. If this is used, then -lincom- and -metaparm- will give confidence intervals for the difference between the z-transformed Kendall's taus, instead of confidence intervals for the difference between the original Kendall's taus. However, both differences have the same sign. It is also possible to use an arcsine transformation, as suggested by Daniels and Kendall (1947).
I hope this helps.
Best wishes
Roger
References
Daniels, H. E., and M. G. Kendall. 1947. The significance of rank correlation where parental correlation exists. Biometrika 34: 197–208.
Edwardes, M. D. d. B. 1995. A confidence interval for Pr(X < Y) − Pr(X > Y) estimated from simple cluster samples. Biometrics 51: 571–578.
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: [email protected]
Web page: http://www.imperial.ac.uk/nhli/r.newson/
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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: [email protected] [mailto:[email protected]] On Behalf Of Mike Lacy
Sent: 05 December 2008 18:30
To: [email protected]
Subject: Re: st: significance test between two kendalls' tau coefficents ?
A
>Date: Thu, 4 Dec 2008 16:13:01 +0000
>From: Ronan Conroy <[email protected]>
>Subject: Re: st: significance test between two kendalls' tau coefficents ?
>
>On 4 Dec 2008, at 13:39, JOHN ANTONAKIS wrote:
>
>> Why don't you simply construct a 95% confidence interval around the
>> tau
>> estimate and check if estimates overlap? STATA reports the ASE for tau
>> with the tab y x, all command.
>
>Warning: overlapping confidence intervals do not necessarily mean that
>the two are not significantly different.
>
>You need the confidence interval for the difference.
Moreover, if you truly want a test as opposed to a CI, it is
worth keeping in mind that the SE of the sampling distribution,
and in fact all aspects of the sampling distribution, is in general
not the same under the null (test situation) as it is under the
alternative (CI situation.)I have seen cases with measures like
Tau in which the two sampling distributions differed radically.
An instructive exercise is to compare the distribution one gets
from -bootstrap- (distribution under the alternative) vs. -permute-
(under the null)
Regards,
Mike Lacy
Fort Collins CO
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