# Lecture 10: Types of Sum of Squares

February 9, 2023 (5th week of classes)

THIS LECTURE IS PRE-RECORDED (VIDEO RECORDINGS BELOW). As a member of the review panel for funding from 2023 to 2025 of The Natural Sciences and Engineering Research Council of Canada, my participation is mandatory.

**Analysis of Covariance (ANCOVA) - part 2 and types of sum of squares**

In this lecture we will continue with ANCOVA and find that when the continuous and discrete predictors are correlated, we need to use different ways to calculate the variation (F-values) and associated p-values.

The common sum-of-squares (called Type I SS; SS stands for sum-of-squares) works when the study is perfectly balanced (i.e., all groups and factors have the same number of observations). This will not be the case when we mix a continuous and a discrete predictor (an in ANCOVAs).

This is also an issue when experiment or observational studies are not fully balanced. This means that the number of observations per combination of factor levels is not equal.

In this lecture, we will cover the issues related to non-orthogonal designs and understand why a different type of sum-of-squares (type III SS) is required in ANCOVA and in non-balanced designs.

Here is a pedagogical guide that I wrote to facilitate the understanding of the issue underlying sum-of-squares. Read this before watching the lecture.

**Recorded lectures**

Download lecture: 3 slides per page and outline

Download lecture: 1 slide per page

pdf with slides contains parts 1 and 2:

**part 1: **Why different sum of squares? Type I and type III sum of squares. You should had read the pedagogical guide (see above for downloading it) before watching this lecture.

**part 2: **Final interpretation of ANCOVAs, assumptions and more complex cases (e.g., when slopes canâ€™t be assumed as parallel)