psych (version 1.0-17)

# 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.

The calculation follows J. Wiggins discussion of personality assessment.

`phi2poly`

## Examples

Run this code
``````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))  }``````

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