Its All on the Square- The Importance of the Sum of Squares and Making the General Linear Model Simple

TL;DR

This paper emphasizes the fundamental role of the sum of squares in the general linear model and advocates for simplifying statistical procedures to enhance understanding and application in scientific research.

Contribution

It introduces a simplified approach to the general linear model focusing on the importance of the sum of squares for clearer comprehension.

Findings

Highlights the central role of the sum of squares in the GLM

Proposes a simplified framework for statistical procedures

Aims to improve statistical understanding and teaching

Abstract

Statistics is one of the most valuable of disciplines. Science is based on proof and it alone produces results, other approaches are not, and do not. Statistics is the only acceptable language of proof in science. Yet statistics is difficult to understand for a large percentage of those who will be evaluating and even doing research. Reasons for this difficulty may be that statistics operates counter to the way people think, as well as the widespread phobia of numeracy. Adding to the difficulty is that undergraduate textbooks tend to make statistical tests seem to be an unorganized conglomeration of unrelated procedures, and this leads to a failure of students to understand that all of the parametric procedures they are studying in an introductory course are ultimately doing the same thing and stem from common sources. In statistics, precisely because the material is complex, the presentation must be simple! This article endeavors to do just that.