ABSTRACT
Because the model is overparameterised (more parameters than can be uniquely estimated from the data), the group effects need to be constrained
in some way, most usually by requiring that ∑ α = =
1 , where k is the num-
ber of groups. The hypothesis of the equality of group means can be written in terms of the group effects as
H0 : α1 = α2 = … = αk = 0 (6.2)
The total variation in the observations is partitioned into that due
observations within groups. Under the hypothesis of the equality of group means, both the between-group variance and the within-group variance are estimates of σ2. Thus, an F-test of the equality of the two variances provides a test of H0. The necessary terms for calculating the required F-test are usually arranged in an analysis of variance table as shown in Table 6.2.
