"Analysis of Variance." A statistical test for heterogeneity of means by analysis of group variances. ANOVA is implemented as ANOVA[data] in the Wolfram Language package ANOVA` .
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
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(2)
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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
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| category |  freedom | SS | mean squared | F-ratio |
| model |  | SSA |  |  |
| error |  | SSE |  | |
| total |  | SST |  |
If the P-value is small, reject the null hypothesis that all means are the same for the different groups.
