phi {psych} | R Documentation |
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.
phi(t, digits = 2)
t |
a 1 x 4 vector or a 2 x 2 matrix |
digits |
round the result to digits |
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.
Given a two x two table of counts
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) )
phi coefficient of correlation
William Revelle with modifications by Leo Gurtler
phi(c(30,20,20,30)) phi(c(40,10,10,40)) x <- matrix(c(40,5,20,20),ncol=2) phi(x)