Once you have chosen between a model I and model II anova, the
next step is to test the homogeneity of means. The null
hypothesis is that the all the groups have the same mean, and
the alternate hypothesis is that at least one of the means is
different from the others. To test the null hypothesis, the
variance of the population is estimated in two different ways.
I'll explain this in a way that is strictly correct only for a
"balanced" one-way anova, one in which the sample size for each
group is the same, but the basic concept is the same for
unbalanced anovas. If the null hypothesis is true, all the
groups are samples from populations with the same mean. One of
the assumptions of the anova is that the populations have the
same variance, too. One way to estimate this variance starts by
calculating the variance within each sample—take the difference
between each observation and its group's mean, square it, then
sum these squared deviates and divide by the number of
observations in the group minus one. Once yo