A complete set of linearly independent functions for the linear model y = X3+ e is a set of rx linearly independent functions X3(k = 1, 2,....rx), where rx is the rank of X, such that all estimable functions can be generated from this set. (i) For the linear model Yij = + a +b; + ij (i=1,2,A; j = 1, 2,..., B) obtain a complete set of linearly inde- pendent estimable functions. (ii) Obtain a complete set of linearly independent estimable functions involving only the a (i = 1, 2,..., A) and show that the sum of squares associated with this set is identical to SS(A) = b(.-..)2, the usual sum of squares for factor A.