The development of inverse normal transformations: a review

Abstract

This paper reviews the literature on inverse normal transformations (INTs), focusing on four primary methods used in regression analysis. We examine the statistical context, derivation and classification of INTs, as well as their applications in business and management. By reflecting on key studies that have shaped the development of these methods, we evaluate whether the choice of INT significantly affects inferential accuracy, particularly when sample sizes are small. We conclude by proposing standardized transformation parameters that bridge theoretical advances and practical decision-making.