To apply the test, assume random sampling of a variate with equal variances,
independent errors, and a normal distribution.
Let be the number of replicates
(sets of identical observations) within each of factor levels (treatment groups),
and be the th observation within factor level . Also assume that the ANOVA is "balanced"
by restricting
to be the same for each factor level.

Now define the sum of square terms

(1)

(2)

(3)

(4)

(5)

which are the total, treatment, and error sums of squares. Here, is the mean of observations within factor
level , and is the "group" mean (i.e., mean of means). Compute
the entries in the following table, obtaining the P-value
corresponding to the calculated F-ratio of the mean squared
values