tet2phi {CorrToolBox} | R Documentation |

## Computation of the Phi Coefficient from the Tetrachoric Correlation

### Description

This function computes the phi coefficient between two variables after both of the variables are dichotomized given the correlation before dichotomization (tetrachoric correlation) as seen in Demirtas (2016). Before computation of the phi coefficient, the specified tetrachoric correlation is compared to the lower and upper correlation bounds of the two continuous variables as defined by the respective skewness and excess kurtosis using the generate, sort and correlate (GSC) algorithm in Demirtas and Hedeker (2011).

### Usage

```
tet2phi(tetcorr, dist1, dist2)
```

### Arguments

`tetcorr` |
The tetrachoric correlation. |

`dist1` |
A list of length 3 containing the skewness, excess kurtosis, and expected value after dichotomization for the first continuous variable with names skewness, exkurtosis, and p, respectively. |

`dist2` |
A list of length 3 containing the skewness, excess kurtosis, and expected value after dichotomization for the second continuous variable with names skewness, exkurtosis, and p, respectively. |

### 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.

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. *The American Statistician*, **65(2)**, 104-109.

### See Also

### 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)
tet2phi(tetcorr=-0.4,
dist1=list(skewness=y1.skew, exkurtosis=y1.exkurt, p=0.85),
dist2=list(skewness=y2.skew, exkurtosis=y2.exkurt, p=0.15))
tet2phi(tetcorr=0.7,
dist1=list(skewness=y1.skew, exkurtosis=y1.exkurt, p=0.10),
dist2=list(skewness=y2.skew, exkurtosis=y2.exkurt, p=0.30))
```

*CorrToolBox*version 1.6.4 Index]