Question: When both factors are random in a two-way ANOVA experiment with K replications per combination of factor levels, the expected mean squares are , and

When both factors are random in a two-way ANOVA experiment with K replications per combination of factor levels, the expected mean squares are

, and

.

a. What F ratio is appropriate for testing versus ?

b. Answer part

(a) for testing versus and versus . HaB: sG H0B: sB 2 . 0 HaA: sA 2 5 0 2 . 0 H0A: sA 2 5 0 HaG: sG 2 . 0 H0G: sG 2 5 0 E(MSAB) 5 s2 1 KsG 2

s2 1 KsG 2 1 JKsA 2, E(MSB) 5 s2 1 KsG 2 1 IKsB 2

E(MSE) 5 s2

, E(MSA) 5

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