phi {psych} R Documentation

## 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

### 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
 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) )

### Value

phi coefficient of correlation

### Author(s)

William Revelle with modifications by Leo Gurtler

### References

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

`phi2poly` ,`Yule`, `Yule2phi`
```phi(c(30,20,20,30))