Article
Regression as the Univariate General Linear Model: Examining Test Statistics, p values, Effect Sizes, and Descriptive Statistics Using R
General Linear Model Journal
(2017)
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, pvalues, and effect sizes associated with the
univariate parametric statistics in the GLM.
Keywords
- Univariate General Linear Model,
- Examining Test Statistics,
- Descriptive Statistics Using R
Disciplines
Publication Date
January 1, 2017
DOI
10.31523/glmj.043001.004
Citation Information
Kim Nimon, Julia Berrios, Greggory Keiffer, Mandolen Mull, et al.. "Regression as the Univariate General Linear Model: Examining Test Statistics, p values, Effect Sizes, and Descriptive Statistics Using R" General Linear Model Journal Vol. 43 Iss. 1 (2017) p. 50 - 82 Available at: http://works.bepress.com/kim-nimon/22/