Sums of Squares

In mathematics, the sum of squares can refer to any set of numbers that has been squared and then added together (i.e., σX2). However, in the statistical analysis of quantitative data, the sum of squared differences or deviations (normally the difference between a score and the mean) is of particular interest. This formulation is usually referred to in research by the term sums of squares. This type of sum of squared values is extremely important in the analysis of the variability in data and in understanding the relationship between variables.

If there is no variability in a set of numbers, then they are all the same. However, this is unlikely to be the case in any research. Indeed, researchers actively investigate changes in their data resulting ...