In Theorem 11.2.5 we saw that the ANOVA null is equivalent to all contrasts being 0. We
Question:
(a) Show that the hypotheses
H0: θ1 = θ2 = ... = θk versus H1: θi, ≠ θj for some i, j
and the hypotheses
H0: θi - θj = 0 for all i, j versus H1: θi - θj ≠ 0 for some i, j
are equivalent.
(b) Express H0 and H1 of the ANOVA test as unions and intersections of the sets
Θij = {θ = (θ1,..., θk) : θi - θj = O}.
Describe how these expressions can be used to construct another (different) union-intersection test of the ANOVA null hypothesis.
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