The tetrachoric correlation is a correlation measure for binary variables and is commonly used in psychometrics, particularly for Item Response Theory (IRT). As with other correlation measures, a tetrachoric correlation ranges between -1 and 1, and describes the association between the two binary variables.
In the following video I discuss the basics on tetrachoric correlation and then work through some examples in R. The R code used in the video is available at the bottom of this page.
Subscribe below to get updates on my latest videos, courses, and other useful information.
library(psych) #for tetrachoric function library(tidyverse) library(openintro) #for resume data # dummy examples x<-matrix(c(30,0,0,30), nrow=2) x tetrachoric(x) y<-matrix(c(0,30,30,0), nrow=2) y tetrachoric(y) z<-matrix(c(45,9,27,16), nrow=2) z tetrachoric(z) # resume data tetrachoric(select(resume, received_callback, military)) tetrachoric(select(resume, received_callback, computer_skills:military)) # doesn't work with string variable tetrachoric(select(resume, received_callback, resume_quality)) # make dummy variable or create table resume <- resume %>% mutate(resume_quality_high=ifelse(resume_quality== "high",1,0)) tetrachoric(select(resume, received_callback, resume_quality_high)) tetrachoric(table(resume$received_callback,resume$resume_quality)) tetra_output<-tetrachoric(table(resume$resume_quality,resume$received_callback)) names(tetra_output) tetra_output$rho