# A generalized (multiple predictor) Taylor-Russell function. Generalized Taylor-Russell Function for Multiple Predictors ```r 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. ## Returns 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. ## Examples ```r # 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) ``` ## 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. ## Author(s) * Niels G. Waller (nwaller@umn.edu)

TaylorRussell function