In the two-way layout of Section 7.5 with a = b = 2, denote the first three terms in the partition of (Xijk − Xij·)

2 by S2 A, S2 B, and S2 AB, corresponding to the A, B, and AB effects (i.e. the α’s, β’s, and γ’s), and denote by HA, HB, and HAB 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 level 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).]