Binomial effect size displays and gain-probability: Alternative ways to interpret hierarchical regression findings, with tutorial.

Abstract

Researchers using a hierarchical regression paradigm enter different variables at different steps in the analysis, each time determining ΔR². Although ΔR² is traditional for both zero-order correlation coefficients and multiple correlation coefficients, it is not the only possibility. It is also possible to use binomial effect size displays and gain-probability analyses to interpret zero-order correlation coefficients. However, nobody has explored the possibility of extending these latter advances from zero-order correlation coefficients to the multiple correlation coefficients obtained in successive steps of hierarchical regression analyses. The present exposition and tutorial show that binomial effect size display and gain-probability interpretations can imply different conclusions both from each other and from ΔR². The message is not that a single interpretation should dominate but that multiple interpretations provide researchers with a more thorough and comprehensive understanding of the implications of the data. (PsycInfo Database Record (c) 2026 APA, all rights reserved).