Regression as the Univariate General Linear Model: Examining Test Statistics, p values, Effect Sizes,and Descriptive Statistics Using R

Abstract

This paper presents regression as the univariate general linear model (GLM). Building on the work of Cohen (1968), McNeil (1974), and Zientek and Thompson (2009), the paper uses descriptive statistics to build a small, simulated dataset that readers can use to verify that multiple linear regression (MLR) subsumes the univariate parametric analyses in the GLM. Unlike other related works, we provide R syntax that demonstrates how MLR produces equivalent test statistics, p values, effect sizes, and descriptive statistics when compared to the univariate analyses that MLR subsumes. The paper diverges from Zientek and Thompson by presenting an expanded hierarchy for MLR and demonstrating why only the case of the chi-square test of independence where the criterion variable is dichotomous, and not the general case, is subsumed by MLR. Readers will find an accessible treatment of the GLM as well as R syntax, which they can use to report descriptive statistics, p values, and effect sizes associated with the univariate parametric statistics in the GLM.