Lecture 10: Types of Sum of Squares

February 12, 2026


Types of sum of squares

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.

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