WITHIN-GROUPS VARIABILITY

We are going to look a little more closely now at the two types of variability we need to consider. Within-groups variability is a measure of how much the observations within a group vary. It is simply the variance of the observations within a group in your sample, and it is used to estimate the variance within a group in the population. (Remember, analysis of variance requires the assumption that all of the groups have the same variance in the population.) Since you do not know if all of the groups have the same mean, you cannot just calculate the variance for all of the cases together. You must calculate the variance for each of the groups individually and then combine these into an "average" variance.

For example, suppose you have three groups of 20 cases each. All 20 cases in the first group have a value of 100, all 20 cases in the second group have a value of 50, and all 20 cases in the third group have a value of 0. Your best guess for the population variance within a group is zero. It appears from your sample that the values of the cases in any particular group do not vary at all. But if you had computed the variance for all of the cases together, it would not even be close to zero. You would calculate the overall mean as 50, and cases in the first and third groups would all vary from this overall mean by 50. There would be plenty of variation.