A representation of orthogonal components in analysis of variance
Clarke, B.R. (2002) A representation of orthogonal components in analysis of variance. International Mathematical Journal, 1 (2). pp. 133-147.
The history of orthogonal components in the analysis of variance and of the Helmert transformation is allied to more recent mathematical representations of Kronecker products. The latter are well known tools useful in the teaching of factorial designs. Presented here are quick derivations of the usual orthogonal projection matrices associated with independent sums of squares for some familiar balanced designs. Succinct representations used to form orthogonal contrasts clearly illustrate the proofs of independence of sums of squares and give obvious interpretation to degrees of freedom. Resultant central and noncentral chi-squared distributions follow easily. A relationship between recursive residuals and the Helmert transformation is also noted.
|Publication Type:||Journal Article|
|Murdoch Affiliation:||School of Mathematical and Physical Sciences|
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