Analysis of covariance for different types of split-plot designs
Date Issued
2009
Date
2009
Author(s)
Jan, Wei-De
Abstract
The correct statistical analysis of a split-plot design with covariate is complicated and the analysis method is not well documented in statistical literature. This paper studies the general methodology for the analyses of covariance for split-plot, split-split plot and split-block designs which are widely used in agrucultural and industrial experiments. The main focus of this study is to construct a mixed model method for the various split-plot designs, to discuss the treatment means adjusted for the covariate, and to calculate the standard errors of the differences between two adjusted treatment means. Existing formulae for the above computations in the statistical literature are called ''algebraic formulae'' and the formulae derived from the mixed model method are called ''matrix formulae'' in this paper. The results from the algebraic formulae are then compared with those from the matix formulae for the hypothetic balanced data. The matric results all coincide with the algebric results. The disadvantage of algebraic method is that the whole set of formulae needs to be extensively modified when the design or the number of covariates changes. Beside, the algebraic formulae can only be used for balanced data (data without missing value). The mixed model method by matrix formulae is free from all the aforementioned difficulties encountered by the algebraic method. Both hypothetical balanced and unbalanced data were used in this study to demonstrate the versatility of the mixed model method.
Subjects
split-plot design
split-split-plot design
split-block design
ANCOVA
mixed model theory
regression coefficient
covariate
Type
thesis
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