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2001 Oct 17
3
Type III sums of squares.
...B to index j.
Let the cell means be mu_ij. (In the overparameterized
notation, mu_ij = mu + alpha_i + beta_j + gamma_ij.)
The hypothesis being tested is
H_0: mu_1.-bar = mu_2.-bar = ... = mu_a.-bar
where factor A has a levels, and ``mu_i.-bar'' means
the average (arithmetic mean) of mu_i1, mu_i2, ..., mu_ib.
(Note --- factor B has b levels.)
I.e. the hypothesis is that there is no difference, on average,
between the levels of A, the average being taken over the levels
of B.
Now taking such an average may not be a sensible thing to do,
but it is perfectly well-defined, and thus a *...