The general nested classification with a constant number of observations per cell, under model II, has the structure Xijk··· = μ + Ai + Bi j + Cijk +···+ Uijk···, i = 1,..., a; j = 1,..., b; k = 1,..., c;....
(i) This can be reduced to a canonical form generalizing (7.45).
(ii) There exist UMP unbiased tests of the hypotheses HA : σ2 A cd...σ2 B+d...σ2 C+···+σ2 ≤ 0, HB : σ2 B d...σ2 C+···+σ2 ≤ 0.