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re: st: -factor- with binary variables

From   Bill Magee <[email protected]>
To   [email protected]
Subject   re: st: -factor- with binary variables
Date   Mon, 29 Nov 2004 04:40:47 -0500

In addition to tetrachoric correlation coefficient, I have read about:
The Phi Correlation Coefficient, which is designed to measure the degree of relation for two variables which are binary (each has only two values --- also called dichotomous).
To compute you first convert your two binary variable into 1's and 0's, and then follow the procedure for Pearson correlation. (

From what I recall, if the proportions coded 1.0 and 0 are close in the 40-60% range, phi performs ok.
The use of the tetrachoric implies assumption of underlying (unassessed) normal distribution. I don't know if there are cases where the phi would outperform the tetrachoric (or on what standards one would evaluate performance) if the tetrachoic assumptions were wrong, but I would be interested in knowing...

bill magee

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