"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
(1)
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(2)
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(3)
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(4)
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(5)
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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
(6)
|
category | 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.