ANOVA Table

The key to our inference procedures is going to use the ANOVA table. This table communicates how much of the variation in the data values comes from variation within groups, and from differences between groups. Any ANOVA table for comparing k groups has the following form:

Source        df        SS            MS     
-------------------------------------------
Between
 Groups      k-1   see below        see below

Within
 Groups      n-k   see below        see below
----------------------------------------------
Total       n-1     see below

To understand the table entries remember that k is the number of groups and n is the total number of response measurements. The df column in the table stands for degrees of freedom, and the SS column stands for sum of squares. As an example, SS Between groups is defined as, . This expression measures how different the group averages ( ) are from the overall average . We call this the variation between groups. The definition for the sum of squares within groups is: . The column denoted MS is called the mean square column and each entry is calculated from taking the appropriate sum of squares and dividing it by the degrees of freedom.