Dear Roger,
1. If I wanted to conduct the somersd test and adjust for age, do I then
need to include a lincom command which provides the age adjusted confidence
interval (see below)? [I referred to p. 10 of params.pdf]
2. In this case, is it more appropriate to chose somersd, rather than tau-a
as the test of association (for an ordered categorical ?
. somersd autism mobility age, tr(z) tdist
. lincom (mobility-age)/2
Results:
. somersd autism mobility age, tr(z) tdist
Somers' D with variable: autism
Transformation: Fisher's z
Valid observations: 305
Degrees of freedom: 304
Symmetric 95% CI for transformed Somers' D
----------------------------------------------------------------------------
| Jackknife
autism | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+--------------------------------------------------------------
mobility | -.3910524 .0899135 -4.35 0.000 -.5679839 -.2141209
Age | .0271106 .0782949 0.35 0.729 -.1269579 .1811791
----------------------------------------------------------------------------
Asymmetric 95% CI for untransformed Somers' D
Somers_D Minimum Maximum
Mobility -.37226715 -.51387713 -.21090749
age .02710392 -.12628019 .1792223
. lincom (mobility - age)/2
(1) .5 mobility - .5 age = 0
----------------------------------------------------------------------------
autism | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+--------------------------------------------------------------
(1) | -.2090815 .0567701 -3.68 0.000 -.3207935 -.0973694
----------------------------------------------------------------------------
Regards,
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
>
>
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