8.22. (Sec. 8.9) The Latin square. Let Yij' i, j = 1, ... , r, be distributed according to N(ll-ij' I), where ooEY,'j = Il-ij ='1 + Ai + Vj + Il-k and k = j - i + 1 (mod r) with L:Aj = L:vj = L:ll-k = O.

(a) Give the univariate analysis of variance table for main effects and error

(including sum~; of squares, numbers of degrees of freedom. and mean squares).

(b) Give the table for the vector case.

(e) Indicate in the vector case how to test the hypothesis Ai = 0, i = l. .... T.