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Analysis of Covariance

  • Ronald ChristensenEmail author
Chapter
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Part of the Springer Texts in Statistics book series (STS)

Abstract

This chapter examines the analysis of partition models, also known as analysis of covariance, a method traditionally used for improving the analysis of designed experiments. Sections 1 and 2 present the theory of estimation and testing for general partitioned models. Sections 3 and 4 present nontraditional applications of the theory. Section 3 applies the partitioned model results to the problem of fixing up balanced ANOVA problems that have lost their balance due to the existence of some missing data. Although applying analysis of covariance to missing data problems is not a traditional experimental design application, it is an application that was used for quite some time until computational improvements made it largely unnecessary. Section 4 uses the analysis of covariance results to derive the analysis for balanced incomplete block designs. Section 5 presents Milliken and Graybill’s (1970) test of a linear model versus a nonlinear alternative. I personally find the techniques of Sections 1 and 2 to be some of the most valuable tools available for deriving results in linear model theory.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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