

Group 
Values 
(observed  overall mean)^{2 } 
(observed  group mean)^{2 } 
(group mean  overall mean)^{2 } 
A 
0 
16 
9 
1 
A 
4 
0 
1 
1 
A 
5 
1 
4 
1 
B 
1 
9 
4 
1 
B 
2 
4 
1 
1 
B 
6 
4 
9 
1 
C 
3 
1 
9 
4 
C 
7 
9 
1 
4 
C 
8 
16 
4 
4 
Sums: 
36 
60 
42 
18 
The question at this point is whether this is the sort of result we would get by a random assignment of items to the various groups or whether it appears that the results seem to be different from what we would usually get by a random assignment. To find out, we compute the F statistics, and then using tables or an Fstatistic calculator, find out the probability of getting a result like the one we have by random chance. (This is, of course, called either a pvalue or a level of significance.)
ANOVA tables are computed as part of regression analysis, which is the primary reason they are included here. They show how much of the original variation in the numbers (the sum of squares around the mean) the regression equation explains and how much of that variation is left unexplained. The Rsquare is computed from the ANOVA results of the regression, and the level of significance that one should attach to it is given by the significance of the Fstatistic.
