Question

a) How is variance partitioned in an analysis of variance? Describe what is included in each type of variability? (b) Why do we partition variance this way? That is, what does partitioning variance this way tell us?

Answer 1

In ANOVA, the total variability is partitioned into its different components namely, variability whose causes can be controlled and variability whose causes cannot be controlled. For this, we consider the total sum of squares and partition into regression sum if squares and error sum of squares. Error sum of square is the random component whose causes are not under control.

This partition helps to identify the causes which can be modified so as to reduce the variability. It also helps to determine the causes which is attributed to purely chance. However the variability due to chance causes is less.