Enhancing the Teaching of Statistics by Use of the Full GLM

Abstract

Increased elegance in math and science is by the use of more comprehensive, easier to understand, and easier to use models. Increasing elegance allows courses to cover more material in greater depth. While the GLM is more elegant than the traditional ANOVA / Regression models, it has in practice been just one more topic added to already filled statistics courses and has had little impact on day-to-day statistical analyses. Introduced in the 1960s - 1970s, its impact has been delayed because it has been necessary to produce a new generation that knew the GLM but could also converse with the pre-1970 generation. When considering a possibly more elegant model, the "full" GLM includes not only GLM -- and therefore ANOVA and regression -- but also chi square contingency table analyses as well as multivariate analyses, and uses the F as the hypothesized variance divided by the error variance in all cases.  Given advancing technology, the computations are now readily done and typically easier than the traditional ANOVA/Regression programs, allowing more focus on issues ranging from how the information is encapsulated so as to best test the hypotheses (by logs, logits, interactions, polynomials, repeated measures as slope or covariates, etc.) to meta-science and the principles of meta-analysis needed to use research literature. And, as expected, the more elegant full GLM means explicitly GLM software can be easier to learn and use.

DOI:10.2458/azu_jmmss_v6i2_gorsuch