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

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.

The calculation follows J. Wiggins discussion of personality assessment.

Value

phi coefficient of correlation

Author(s)

William Revelle with modifications by Leo Gurtler

See Also

phi2poly

Examples

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

## The function is currently defined as
function(t,digits=2)
{  # expects: t is a 2 x 2 matrix or a vector of length(4)
   stopifnot(prod(dim(t)) == 4 || length(t) == 4)
   if(is.vector(t)) t <- matrix(t, 2)
   r.sum <- rowSums(t)
   c.sum <- colSums(t)
   total <- sum(r.sum)
   r.sum <- r.sum/total
   c.sum <- c.sum/total
   v <- prod(r.sum, c.sum)
   phi <- (t[1,1]/total - c.sum[1]*r.sum[1]) /sqrt(v)
return(round(phi,2))  }