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Nonorthogonal Analysis of Variance using a Generalized Conjugate-Gradient Algorithm

Gene H. Golub and Stephen G. Nash
Journal of the American Statistical Association
Vol. 77, No. 377 (Mar., 1982), pp. 109-116
DOI: 10.2307/2287776
Stable URL: http://www.jstor.org/stable/2287776
Page Count: 8
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Nonorthogonal Analysis of Variance using a Generalized Conjugate-Gradient Algorithm
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Abstract

A method is developed that computes an exact nonorthogonal analysis of variance using cell means. The method is iterative and does not require that the nonorthogonal design matrix be stored or formed. At each stage in the process, a balanced analysis of variance problem must be solved. A monotonicity property for the estimates of the regression sum of squares is derived that could be used to minimize iteration in hypothesis testing. An application of the algorithm to the solution of analysis of covariance problems is also given.

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