Convert AUC to a rank-biserial correlation

Converts the area under the ROC curve to the rank-biserial correlation, \(r_{rb} = 2 AUC - 1\). This is a distribution-free dominance summary: it rescales the probability that a randomly chosen successful applicant is ranked above a randomly chosen unsuccessful applicant from the [0, 1] AUC scale to the [-1, 1] correlation-like scale.

Usage

auc_to_rank_biserial(auc)

Arguments

auc

Area under the ROC curve. Must be in [0, 1].

Value

Numeric vector of rank-biserial correlations.

References

Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143(1), 29-36.

Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11.IT.3.1.

Rice, M. E., & Harris, G. T. (2005). Comparing effect sizes in follow-up studies: ROC area, Cohen's d, and r. Law and Human Behavior, 29(5), 615-620.

Examples

# Minimal example: AUC = .50 implies no dominance.
auc_to_rank_biserial(.50)
#> [1] 0

# AUC = .75 means 75% favorable pairwise ordering; r_rb = .50.
auc_to_rank_biserial(.75)
#> [1] 0.5