Re: st: Can Spearman's rho be used to measure of the degree of association between two binary variables ?

[Marcos Vinicius <bioestatistico@inbox.com>]

Hello,
Thank you everyone for the replies.
I am a luck person participating in this group with brilhant minds. ..Always inspiring and incentivating me in this fields of biostatistics.
Have a nice week,
MArcos Vinicius.
> -----Original Message-----
> From: dirk.enzmann@uni-hamburg.de
> Sent: Mon, 21 May 2012 15:47:44 +0200
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Can Spearman's rho be used to measure of the degree of
> association between two binary variables ?
> 
> Marcos Vinicius asked, whether Spearman's rho can be used to measure the
> degree of association between two binary variables, see:
> 
> http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-836.html
> 
> to which he received very helpful answers (perhaps more than he
> initially wanted to know):
> 
> - from Maarten Buis and Richard Williams
> http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-855.html
> http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-859.html
> who discuss whether multicollinearity should be regarded as a problem at
> all
> 
> - and from Cameron McIntosh, Richard Stoll, and Roger Newson
> http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-837.html
> http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-838.html
> http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-858.html
> who point at alternative measures for the association of two binary
> variables.
> 
> Let me add two comments as to the use of tetrachoric (or polychoric)
> correlation coefficients vs. Pearson (or Spearman) correlation
> coefficients in the case of two binary variables:
> 1) Tetrachoric and Pearson correlations answer different questions: The
> first estimates the correlation of two *latent* (quasi-continuous)
> variables "behind" the observed dichotomous variables, thus assuming
> that both variables are artificially dichotomous, whereas the Pearson
> coefficients shows how the *observed* values correlate, thus assuming
> naturally dichotomous variables.
> 2) Ledesma et al. (2011) (see:
> http://openjournal.konradlorenz.edu.co/index.php/rlpsi/article/viewFile/459/463
> ) cited by Cameron write: "Stata gives their users a function based on a
> work by Edwards and Edwards (1984), that is basically 'a very rough
> approximation' and
> is consequently unsuitable for many applications ..." (p. 182). This is
> not quite correct: Stata computes the tetrachoric correlation "... by
> using the Edwards and Edwards (1984) noniterative estimator as the
> *initial* value" (see: [R] Base Referencence, p. 2196; bold face by me)
> - the coefficient calculated by Stata is at least as precise as the
> coefficient calculated by Ledesma et al.'s Vista-Tetrachor program:
> 
> * --- Example from Ledesma et al., p. 183 ------------------------
> input y x ncases
> 1 1 203
> 1 0 186
> 0 1 167
> 0 0 374
> end
> expand ncases
> tetrachoric x y
> * --- End of Stata example ---------------------------------------
> 
> Dirk
> 
> ========================================
> Dr. Dirk Enzmann
> Institute of Criminal Sciences
> Dept. of Criminology
> Rothenbaumchaussee 33
> D-20148 Hamburg
> Germany
> 
> phone: +49-(0)40-42838.7498 (office)
>         +49-(0)40-42838.4591 (Mrs Billon)
> fax:   +49-(0)40-42838.2344
> email: dirk.enzmann@uni-hamburg.de
> http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html
> ========================================
> *
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