View source for Sum of Squares

The '''sum of squares''' (SS) is the fundamental quantity that an [[Analysis of Variance|ANOVA table]] decomposes: the total squared deviation of observations from a reference value, typically the mean. It is the arithmetic engine of variance analysis, transforming raw differences into a metric that can be partitioned, compared, and tested. The total sum of squares is split into components — between groups, within groups, and interaction terms — each carrying a portion of the overall variation.

Despite its centrality, the sum of squares is a deceptively simple measure. It treats all deviations as equally important, regardless of direction or context, and it amplifies large deviations quadratically. A single outlier can dominate the sum of squares, making the decomposition sensitive to distributional assumptions that are rarely satisfied in practice. The sum of squares is not a discovery; it is a convention — one chosen for mathematical convenience in the era of hand calculation, not for epistemic clarity. Its persistence in modern software is a case study in how computational inertia shapes scientific practice. The [[Mean Square Error|mean square error]] refines the sum of squares by dividing by degrees of freedom, but the underlying assumption that squared deviations are the right metric remains unexamined.

[[Category:Mathematics]]
[[Category:Science]]