psych (version 1.0-77)

phi: Find the phi coefficient of correlation between two dichotomous variables

Description

Given a 1 x 4 vector or a 2 x 2 matrix of frequencies, find the phi coefficient of correlation. Typical use is in the case of predicting a dichotomous criterion from a dichotomous predictor.

Usage

phi(t, digits = 2)

Arguments

t

a 1 x 4 vector or a 2 x 2 matrix

digits

round the result to digits

Value

• phi coefficient of correlation

Details

In many prediction situations, a dichotomous predictor (accept/reject) is validated against a dichotomous criterion (success/failure). Although a polychoric correlation estimates the underlying Pearson correlation as if the predictor and criteria were continuous and bivariate normal variables, the phi coefficient is the Pearson applied to a matrix of 0's and 1s.

For a very useful discussion of various measures of association given a 2 x 2 table, and why one should probably prefer the Yule coefficient, see Warren (2008).

Given a two x two table of counts llll{ a b a+b c d c+d a+c b+d a+b+c+d } convert all counts to fractions of the total and then \ Phi = a- (a+b)*(a+c)/sqrt((a+b)(c+d)(a+c)(b+d) )

References

Warrens, Matthijs (2008), On Association Coefficients for 2x2 Tables and Properties That Do Not Depend on the Marginal Distributions. Psychometrika, 73, 777-789.

See Also

phi2poly ,Yule, Yule2phi

Examples

phi(c(30,20,20,30))
phi(c(40,10,10,40))
x <- matrix(c(40,5,20,20),ncol=2)
phi(x)