Convert AUC to a point-biserial correlation — auc_to_point

Converts AUC to Cohen's d under the equal-variance binormal model and then converts d to a point-biserial correlation for a user-specified base rate. This is the preferred correlation-like conversion when a utility-analysis function requires a validity input but the available evidence is reported as AUC.

Usage

auc_to_point_biserial(auc, base_rate = 0.5)

Arguments

auc: Area under the ROC curve. Must be in (0, 1) because AUC values of 0 or 1 imply infinite d under the equal-variance binormal model.
base_rate: Proportion in the focal or successful group, usually denoted \(p\). Must be in (0, 1). The default is .50.

Value

Numeric vector of point-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.

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.

Salgado, J. F. (2018). Transforming the area under the normal curve (AUC) into Cohen's d, Pearson's r_pb, odds-ratio, and natural log odds-ratio: Two conversion tables. The European Journal of Psychology Applied to Legal Context, 10(1), 35-47.

Examples

# Minimal example: AUC to d, then to r_pb for a balanced binary criterion.
auc_to_point_biserial(.75)
#> [1] 0.4304822

# Substantive example: examine how base rate affects the implied r_pb.
auc_to_point_biserial(.75, base_rate = c(.50, .30, .20, .10))
#> [1] 0.4304822 0.4005260 0.3564821 0.2751188