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.

### 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)

[Package

*psych* version 1.0-68

Index]