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General Analysis of Covariance Models for the Split Block and Related Block Designs
Author(s) -
Monlezun C. J.,
Blouin D. C.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300606
Subject(s) - mathematics , covariate , statistics , analysis of covariance , covariance , test statistic , confidence interval , degrees of freedom (physics and chemistry) , block design , block (permutation group theory) , statistic , analysis of variance , statistical hypothesis testing , combinatorics , physics , quantum mechanics
Abstract Exact test statistics and confidence intervals for a general split block ANOCOVA model are derived. With a single covariate, each statistic for testing main effect A , main effect B , and the AxB interaction has one less numerator degree of freedom than its counterpart in the ordinary ANOVA without a covariate. Sufficient conditions on the model parameters which allow these lost numerator degrees of freedom to be regained are given, as are exact statistics and confidence intervals for the corresponding reduced models. A note of caution is offered when constructing test statistics for reduced versions of the general model using the method of generalized least squares. General analysis of covariance models for two other block designs are presented.