A Confidence Interval for the Difference Between Standardized Regression Coefficients

Abstract

Researchers are often interested in comparing predictors, a practice commonly done via informal comparisons of standardized regression slopes. However, formal interval-based approaches offer advantages over informal comparison. Specifically, this article examines a delta-method-based confidence interval for the difference between two standardized regression coefficients, building upon previous work on confidence intervals for single coefficients. Using Monte Carlo simulation studies, the proposed approach is evaluated at finite sample sizes with respect to coverage rate, interval width, Type I error rate, and statistical power under a variety of conditions, and is shown to outperform an alternative approach that uses the standard covariance matrix found in regression textbooks. Additional simulations evaluate current software implementations, small sample performance, and multiple comparison procedures for simultaneously testing multiple differences of interest. Guidance on sample size planning for narrow confidence intervals, an R function to conduct the proposed method, and two empirical demonstrations are provided. The goal is to offer researchers a different tool in their toolbox for when comparisons among standardized coefficients are desired, as a supplement to, rather than a replacement for, other potentially useful analyses.