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Assume that H0 in (11.6.5) is true; that is, all observations have the same mean μ. Prove that S2Betw/σ2 has the χ2 distribution with p − 1 degrees of freedom. Let
then use the same method that was used in Sec. 8.3 to find the distribution of the sample variance. You may use the following fact without proving it:
Let u = ((n1/n)1/2, . . . , (np/n)1/2). Then there exists an orthogonal matrix A whose first row is u. |
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