When sample sizes are equal (Ji J), the parameters 1, 2, .

Chapter 10, Problem 10.29

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When sample sizes are equal (Ji J), the parameters 1, 2, . . . , I of the alternative parameterization are restricted by i 0. For unequal sample sizes, the most natural restriction is Ji i 0. Use this to show that E(MSTr) 2 Ji 2 i What is E(MSTr) when H0 is true? [This expectation is correct if Ji i 0 is replaced by the restriction i 0 (or any other single linear restriction on the is used to reduce the model to I independent parameters), but Ji i 0 simplifies the algebra and yields natural estimates for the model parameters (in particular, i x ix).] 30

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