Yule: From a two by two table, find the Yule coefficients of association, convert to phi, or polychoric, recreate table the table to create the Yule coefficient.

Description

One of the many measures of association is the Yule coefficient. Given a two x two table of counts lll{ a b c d } Yule Q is (ad - bc)/(ad+bc). Conceptually, this is the number of pairs in agreement (ad) - the number in disagreement (bc) over the total number of paired observations. ad/bc is the odds ratio and Q = (OR-1)/(OR+1) Yule's coefficient of colligation is Y = (sqrt(OR) - 1)/(sqrt(OR)+1) Yule.inv finds the cell entries for a particular Q and the marginals (a+b,c+d,a+c, b+d). This is useful for converting old tables of correlations into more conventional phi or polychoric correlations. Yule2phi and Yule2poly convert the Yule Q with set marginals to the correponding phi or polychoric correlation.

Usage

Yule(x,Y=FALSE)
Yule.inv(Q,m)
Yule2phi(Q,m)
Yule2poly(Q,m)

Arguments

A vector of four elements or a two by two matrix

Y=TRUE return Yule's Y coefficient of colligation

The Yule coefficient

A two x two matrix of marginals or a four element vector of marginals

Value

QThe Yule Q coefficient
RA two by two matrix of counts

Details

Yule developed two measures of association for two by two tables. Both are functions of the odds ratio

References

Yule, G. Uday (1912) On the methods of measuring association between two attributes. Journal of the Royal Statistical Society, LXXV, 579-652

Examples

Run this code

Nach <- matrix(c(40,10,20,50),ncol=2,byrow=TRUE)
Yule(Nach)
Yule.inv(.81818,c(50,70,60,60))
Yule2phi(.81818,c(50,70,60,60))
if(require(polycor)) Yule2poly(.81818,c(50,70,60,60))
phi(Nach)  #much less

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