Analysis of Covariance: Its Nature and Uses

TLDR

Analysis of covariance merges the strengths of regression and analysis of variance, reconciling their requirements. The paper introduces the analysis of covariance, outlining its nature, principal uses, and standard methods and significance tests. It is illustrated by a two-way classification with treatments as rows and blocks or replications as columns, employing a standard mathematical model.

Abstract

This paper is intended as an introduction to the subsequent papers in this issue. It discusses the nature and principal uses of the analysis of covariance, and presents the standard methods and tests of significance. As Fisher [1934] has expressed it, the analysis of covariance combines the advantages and reconciles the requirements of the two very widely applicable procedures known as regression and analysis of variance. This dual role can be illustrated by a two-way classification in which rows represent treatments, and columns represent blocks or replications. The typical mathematical model appropriate to the analysis of covariance is