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

			(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

(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.