23. In the two-way layout of Section 6 with a = b = 2, denote the first three terms in the partition of EEE(X;jk - X;j.)2 by S;, SJ, and SiB' corresponding to the A, B, and AB effects (i.e. the a's, {J's, and y's), and denote by HA , HB , and HA R the hypotheses of these effects being zero. Define a new two-level factor B' which is at level 1 when A and B are both at level 1 or both at leve 2, and which is at level 2 when A and B are at different levels. Then HB• = HAB , SB ' = SAB' HAB, = HB , SAB' = SB' so that the B-effect has become an interaction, and the AB-interaction the effect of the factor B'. [Shaffer (1977b).]