corrZ2phi {CorrToolBox} R Documentation

## Computation of the Phi Coefficient from the Correlation of Bivariate Standard Normal Variables

### Description

This function computes the phi coefficient derived from dichotomizing bivariate standard normal variables.

### Usage

corrZ2phi(corrZ, p1, p2)


### Arguments

 corrZ The correlation of two standard normal variables. p1 The expected value of the first variable after dichotomization. p2 The expected value of the second variable after dichotomization.

### Value

The phi coefficient.

### References

Demirtas, H. (2016). A note on the relationship between the phi coefficient and the tetrachoric correlation under nonnormal underlying distributions. The American Statistician, 70(2), 143-148.

tet2phi

### Examples

set.seed(987)
library(moments)

y1<-rweibull(n=100000, scale=1, shape=1)
y1.skew<-round(skewness(y1), 5)
y1.exkurt<-round(kurtosis(y1)-3, 5)

gaussmix <- function(n,m1,m2,s1,s2,pi) {
I <- runif(n)<pi
rnorm(n,mean=ifelse(I,m1,m2),sd=ifelse(I,s1,s2))
}
y2<-gaussmix(n=100000, m1=0, s1=1, m2=3, s2=1, pi=0.5)
y2.skew<-round(skewness(y2), 5)
y2.exkurt<-round(kurtosis(y2)-3, 5)

corrZ2phi(corrZ=-0.456, p1=0.85, p2=0.15)


[Package CorrToolBox version 1.6.4 Index]