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Establishing χ2 Properties of Sums of Squares Using Induction

Shayle R. Searle and Friedrich Pukelsheim
The American Statistician
Vol. 39, No. 4, Part 1 (Nov., 1985), pp. 301-303
DOI: 10.2307/2683710
Stable URL: http://www.jstor.org/stable/2683710
Page Count: 3
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Establishing χ2 Properties of Sums of Squares Using Induction
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Abstract

The between-classes sum of squares in a between- and within-classes analysis of variance has, under normality, a χ2 distribution. Although "substantial mathematical machinery" (Stigler 1984) is often used in classroom derivation of this distribution, it can be avoided by using induction and independence properties of standard normal variables. This is the derivation given here for unequal subclass numbers data. Independence of the between- and within-classes sums of squares is also shown.

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