Computes the Taylor-Russell classification table for one normally distributed predictor and one dichotomized criterion.
Value
A list with thresholds, TP, FP, FN, TN, PPV, sensitivity, specificity, and incremental success over the base rate.
References
Taylor, H. C., & Russell, J. T. (1939). The relationship of validity coefficients to the practical effectiveness of tests in selection. Journal of Applied Psychology, 23, 565-578.
Cascio, W. F. (1980). Responding to the demand for accountability: A critical analysis of three utility models. Organizational Behavior and Human Performance, 25, 32-45.
Examples
# Literature: Taylor and Russell (1939); Cascio (1980).
# Use the first call as a minimal example; the longer block illustrates
# how to interpret the function in the substantive setting discussed in the literature.
# Minimal example (Taylor and Russell (1939); Cascio (1980)).
tr_classic(base_rate = .50, selection_ratio = .20, validity = .35)
#> <psu_tr>
#> base_rate: 0.5
#> selection_ratio: 0.2
#> validity: 0.35
#> predictor_cutoff_z: 0.841621
#> criterion_cutoff_z: 0
#> true_positive: 0.13931
#> false_positive: 0.0606895
#> false_negative: 0.36069
#> true_negative: 0.43931
#> ppv: 0.696552
#> success_ratio: 0.696552
#> incremental_success: 0.196552
#> sensitivity: 0.278621
#> specificity: 0.878621
#> digits: 3
# Substantive example (Taylor and Russell, 1939; Cascio, 1980).
# Examine how selectivity changes the success ratio.
low_sr <- tr_classic(base_rate = .50, selection_ratio = .10, validity = .35)
high_sr <- tr_classic(base_rate = .50, selection_ratio = .50, validity = .35)
c(low_selection_ratio = low_sr$ppv, high_selection_ratio = high_sr$ppv)
#> low_selection_ratio high_selection_ratio
#> 0.7414190 0.6138184