corrZ2phi {CorrToolBox}

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.

See Also

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)