## Analysis of Variance

The **Analysis of Variance** table summarizes the information
related to the sources of variation in the data.
**Sum of Squares** measures variation present in the data.
It is calculated by summing squared deviations.
There are three sources of variation:
**Model**, **Error**, and **C Total**.
The **Model** row in the table corresponds
to the variation *among* class means.
The **Error** row corresponds to in the model
and represents variation *within* class means.
**C Total** is the total sum of squares corrected for
the mean, and it is the sum of **Model** and **Error**.
Degrees of Freedom, **DF**, are associated with each
sum of squares and are related in the same way.
**Mean Square** is the **Sum of Squares** divided by its
associated **DF** (Moore and McCabe 1989, p.685).
If the data are normally distributed, the ratio of
the **Mean Square** for the **Model** to the **Mean Square**
for **Error** is an *F statistic*.
This *F* statistic tests the null hypothesis
that all the class means are the same against the
alternative hypothesis that the means are not all equal.
Think of the ratio as a comparison of the variation
*among* class means to variation *within* class means.
The larger the ratio, the more evidence
that the means are not the same.
The computed *F* statistic (labeled **F Stat**) is **6.0276**.
You can use the *p*-value (labeled **Pr > F**)
to determine whether to reject the null hypothesis.
The *p-value*, also referred to as the
*probability value* or *observed significance level*,
is the probability of obtaining (by chance alone)
an *F* statistic greater than the computed
*F* statistic when the null hypothesis is true.
The smaller the *p*-value, the stronger
the evidence against the null hypothesis.
In this example, the *p*-value is so small that you
can clearly reject the null hypothesis
and conclude
that at least one of the class means is different.
At this point, you have demonstrated statistical
significance but cannot make statements about
which class means are different.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.