ANOVA
"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
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
 |
(6)
|
| 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.
REFERENCES:
Miller, R. G. Beyond ANOVA: Basics of Applied Statistics. Boca Raton, FL: Chapman & Hall, 1997.
