TOPICS
Search

Statistical Sum of Squares


A statistical sum of squares measures variation by adding squared deviations. For observations y_1, y_2, ..., y_n with sample mean y^_, the total sum of squares is

 SS_(total)=sum_(i=1)^n(y_i-y^_)^2.

In an analysis of variance, this total is partitioned into sums of squares associated with sources of variation and error. Dividing a source sum of squares by its degrees of freedom gives the corresponding mean square.


See also

ANOVA, ANOVA Table, Degree of Freedom, Sample Mean, Variance

Explore with Wolfram|Alpha

References

Montgomery, D. C. Design and Analysis of Experiments, 8th ed. Hoboken, NJ: Wiley, 2013.

Cite this as:

Weisstein, Eric W. "Statistical Sum of Squares." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StatisticalSumofSquares.html

Subject classifications