[R] Polychoric and tetrachoric correlation

John Fox jfox at mcmaster.ca
Wed Sep 3 04:47:14 CEST 2008

Dear Andy,

Yes, the tetrachoric correlation is a special case of the polychoric
correlation when both factors are dichotomous.

The 95-percent confidence interval that you suggest might be adequate if the
sample size is sufficiently large and the correlation isn't too close to 0
or 1, but it is probably not in general terribly trustworthy.

I hope this helps,


Original message:

Andy Fugard a.fugard at ed.ac.uk 
Mon Sep 1 19:25:54 CEST 2008 

Hi there,

Am I correct to believe that tetrachoric correlation is a special case 
of polychoric correlation when there are only two levels to the ordered 
factor?  Thus it should be okay to use hetcor from the polycor package 
to build a matrix of correlations for binary variables?

If this is true, how can one estimate 95% confidence intervals for the 
correlations?  My guess would be

   mat = hetcor(dataframe)

   mat$correlation - (1.96 * mat$std.errors)
   mat$correlation + (1.96 * mat$std.errors)



Andy Fugard, Postgraduate Research Student
Psychology (Room S6), The University of Edinburgh,
   7 George Square, Edinburgh EH8 9JZ, UK
+44 (0)78 123 87190   http://figuraleffect.googlepages.com/

The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.

John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox

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