Consider the two-factor model with interaction
yij = + i + j + ij :
Suppose that there are a and b levels of the factors respectively. Now consider the set of equations
ij ?? 1j ?? i1 + 11 = 0; i = 2; : : : ; a; j = 2; : : : ; b:
(a) Show that the equations are not redundant.
(b) Show that these equations are equivalent to the hypothesis of no interaction.
(c) Thereby calculate the rank of the hypothesis of no interaction.
(d) Show that the hypothesis is testable, provided there exists at least one sample from each
combination of factor levels.