TaylorRussell {TaylorRussell}

A generalized (multiple predictor) Taylor-Russell function.

Description

Generalized Taylor-Russell Function for Multiple Predictors

Usage

TaylorRussell(SR = NULL, BR = NULL, R = NULL, PrintLevel = 0, Digits = 3)

Arguments

SR

(vector) A vector of Selection Ratios for N selection tests.

BR

(scalar) The Base Rate of criterion performance.

R

(matrix) An (N + 1) x (N + 1) correlation matrix in which the predictor/criterion correlations are in column N + 1 of R.

PrintLevel

(integer). If PrintLevel = 0 then no output is printed to screen. If PrintLevel > 0 then output is printed to screen. Defaults to PrintLevel = 0.

Digits

(integer) The number of significant digits in the printed output.

Value

The following output variables are returned.

• BR: (scalar) The Base Rate of criterion performance.

• SR: (vector) The user-defined vector of predictor Selection Ratios.

• R: (matrix) The input correlation matrix.

• TP: (scalar) The percentage of True Positives.

• FP: (scalar) The percentage of False Positives.

• TN: (scalar) The percentage of True Negatives.

• FN: (scalar) The percentage of False Negatives.

• Accepted: The percentage of selected individuals (i.e., TP + FP).

• PPV: The Positive Predictive Value. This is the probability that a selected individual is a True Positive.

• Sensitivity: The test battery Sensitivity rate. This is the probability that a person who is acceptable on the criterion is called acceptable by the test battery.

• Specificity: The test battery Specificity rate. This is the probability that a person who falls below the criterion threshold is deemed unacceptable by the test battery.

Author(s)

• Niels G. Waller ([e-mail])

References

• Taylor, H. C. & Russell, J. (1939). The relationship of validity coefficients to the practical effectiveness of tests in selection: Discussion and tables. Journal of Applied Psychology, 23(5), 565–578.

• Thomas, J. G., Owen, D., & Gunst, R. (1977). Improving the use of educational tests as selection tools. Journal of Educational Statistics, 2(1), 55–77.

Examples

# Example 1
# Reproduce Table 3 (p. 574) of Taylor and Russell

r <- seq(0, 1, by = .05)
sr <- c(.05, seq(.10, .90, by = .10), .95)
num.r <- length(r)
num.sr <- length(sr)

old <- options(width = 132)

Table3 <- matrix(0, num.r, num.sr)
for(i in 1 : num.r){
   for(j in 1:num.sr){
   
     Table3[i,j] <-  TaylorRussell(
                       SR = sr[j],
                       BR = .20, 
                       R = matrix(c(1, r[i], r[i], 1), 2, 2), 
                       PrintLevel = 0,
                       Digits = 3)$PPV  
   
  }# END over j
}# END over i

rownames(Table3) <- r
colnames(Table3) <- sr
Table3 |> round(2)

# Example 2
# Thomas, Owen, & Gunst (1977) -- Example 1: Criterion = GPA

R <- matrix(c(1, .5, .7,
             .5, 1, .7,
            .7, .7, 1), 3, 3)

 # See Table 6: Target Acceptance = 20%
 out.20 <- TaylorRussell(
 SR = c(.354, .354),  # the marginal probabilities
 BR = .60, 
 R = R,
 PrintLevel = 1) 

# See Table 6:  Target Acceptance = 50%
out.50 <- TaylorRussell(
 SR = c(.653, .653),   # the marginal probabilities
 BR = .60, 
 R = R,
 PrintLevel = 1) 
 
 options(old)