Total sum of squares
In statistical data analysis the total sum of squares is a quantity that appears as part of a standard way of presenting results of such analyses. For a set of observations, it is defined as the sum over all squared differences between the observations and their overall mean.:
For wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares. For a proof of this in the multivariate OLS case, see partitioning in the general OLS model.
In analysis of variance the total sum of squares is the sum of the so-called "within-samples" sum of squares and "between-samples" sum of squares, i.e., partitioning of the sum of squares.
In multivariate analysis of variance the following equation applies
where T is the total sum of squares and products matrix, W is the within-samples SSP matrix and B is the between-samples SSP matrix.
Similar terminology may also be used in linear discriminant analysis, where W and B are respectively referred to as the within-groups and between-groups SSP matrices.
