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help for ^somersd^                                                (STB-55: snp15)
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Somers' D or Kendall's tau-a with confidence intervals
-------------------------------------------------------

	^somersd^     varlist [weight] [^if^ exp] [^in^ range]
			[^,^ ^cl^uster^(^varname^)^ ^l^evel^(^#^)^ ^ta^ua  ^td^ist
			^tr^ansf^(^transformation_name^)^]

where transformation_name is one of

	^iden^ | ^z^ | ^asin^ | ^rho^ | ^zrho^

^fweight^s, ^iweight^s and ^pweight^s are allowed; see help @weights@.


Description
-----------

^somersd^ calculates values of Somers' D or Kendall's tau-a for the
first variable of varlist as a predictor of each of the other variables
in varlist, with estimates and jackknife variances and confidence
intervals output as if for the parameters of a maximum likelihood fit.
It is possible to use ^lincom^ to output confidence limits for differences
between the population Somers' D or tau-a values.

Options for use with ^somersd^
----------------------------

^cluster(^varname^)^ specifies the variable which defines sampling clusters.
    If ^cluster^ is defined, then the between-cluster Somers' D or tau-a is
    calculated, and the variances are calculated assuming that the data
    are sampled independently from a population of clusters, rather than
    from a population of observations.

^level(^#^)^ specifies the confidence level, in percent, for confidence
    intervals of the estimates; see ^help level^.

^taua^ causes ^somersd^ to calculate Kendall's tau-a. If ^taua^ is absent,
    then Somers' D is calculated.

^tdist^ specifies that the estimates are assumed to have a
    t-distribution with n-1 degrees of freedom, where n is the number of
    clusters, or the number of observations if ^cluster^ is not specified.

^transf(^transformation_name^)^ specifies that the estimates are to be
    transformed, defining a confidence level for the transformed population
    value. ^iden^ (identity or untransformed) is the default. ^z^
    specifies Fisher's z (the hyperbolic arctangent), ^asin^ specifies
    Daniels' arcsine, ^rho^ specifies Greiner's rho (Pearson correlation
    estimated using Greiner's relation), and ^zrho^ specifies the
    z-transform of Greiner's rho.


Remarks
-------

Somers' D is defined as

^D(Y|X)=tau-a(X,Y)/tau-a(X,X)^

In the case of a binary x-variable, Somers' D is the parameter tested
for a zero value by the Mann-Whitney U-test. In the case of paired
data, the Wilcoxon paired ranksum test tests a zero value for D(Y|X),
where X is the sign of a paired difference and Y is the absolute value
of the same paired difference.

The covariance matrix is estimated by jackknifing the underlying
U-statistics, as described in Arvesen (1969). Taylor polynomials are used
to calculate variances for Kendall's tau-a, Somers' D values and their
transformations.


Examples
--------

 . ^somersd foreign mpg weight^

 . ^somersd foreign mpg weight,tr(z)^

 . ^somersd mpg weight displ,taua tr(z) cluster(manuf)^


Author
------

        Roger Newson
        Guy's, King's and St Thomas' School of Medicine, London, UK.
        email: roger.newson@@kcl.ac.uk


References
----------

Arvesen JN. 1969. Jackknifing U-statistics. Annals of Mathematical Statistics
    40: 2076-2100.


Also see
--------

   STB: STB-55 snp15
Manual: ^[R] spearman, [R] signrank^