##########################
# Taylor & Russell
##########################


### Specify three values
sr <- 0.05 # Selection Ratio
br <- 0.2 # Base Rate
r <- 0.7 # Predictive Validity

####### Calculation #############
library(mvtnorm)
zx <- qnorm(1 - sr)
zy <- qnorm(1 - br)
r <- matrix(c(1, r, r, 1), 2, 2)
q1 <- pmvnorm(lower = c(zx, zy), mean=c(0,0), corr=r)
q1q4 <- pmvnorm(lower = c(zx, -Inf), mean=c(0,0), corr=r)
q1/q1q4



#########################
# Naylor & Shines
#########################

### Specify two values
sr <- 0.7 # Selection Ratio
r <- 0.7 # Predictive Validity

####### Calculation #############
zx <- qnorm(1 - sr)
lambda <- dnorm(zx)
r * lambda / sr

#########################
# Calculation Example
#########################

### Specify two values
sr <- 0.5 # Selection Ratio
r <- 0.4 # Predictive Validity

####### Calculation #############
zx <- qnorm(1 - sr)
lambda <- dnorm(zx)
r * lambda / sr