Analysis of Covariance

Introduction

The Analysis of Covariance (generally known as ANCOVA) is a statistical methodology for incorporating quantitatively measured independent observed (not controlled) variables in a designed experiment. Such a quantitatively measured independent observed variable is generally referred to as a covariate (hence the name of the methodology – analysis of covariance). Covariates are also referred to as concomitant variables or control variables.

If we denote the general linear model (GLM) associated with a completely randomized design as

$${Y }_{ij} = \mu + {\tau }_{j} + {\epsilon }_{ij},\ i = 1,\ldots ,{n}_{j},\ j = 1,\ldots ,m$$

where

• Y _ij = the ith observed value of the response variable at the jth treatment level

• μ = a constant common to all observations

• τ _j = the effect of the jth treatment level

• ε _ij = the random variation attributable to all uncontrolled influences on the ith observed value of the response variable at the jth treatment level

For this model the within group...