Convert AUC to Cohen's d under the equal-variance binormal model — auc_to_d_equal

Converts AUC to Cohen's d using \(d = \sqrt{2}\Phi^{-1}(AUC)\). This conversion assumes two normal distributions with equal variances and should therefore be interpreted as a model-based effect-size conversion, not as a universal transformation from classifier accuracy to personnel-selection validity.

Usage

auc_to_d_equal_variance(auc)

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.

Value

Numeric vector of Cohen's d values.

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 based on the equal-variance binormal conversion.
auc_to_d_equal_variance(.75)
#> [1] 0.9538726

# Direction is preserved: AUC below .50 implies a negative effect.
auc_to_d_equal_variance(.40)
#> [1] -0.3582869