Analysis of covariance: A useful technique for analyzing quality improvement experiments

The analysis of covariance (ANCOVA) is an often overlooked analytical and modelling tool useful for designed experiments. ANCOVA is a combination of regression analysis and the analysis of variance. It is used to increase the precision of a model fit when an uncontrollable but observable nuisance variables has an impact on the response variable. This paper provides an introductory tutorial on ANCOVA methodology. We present the ANCOVA methodology from an algebraic and graphical viewpoint as well as discuss general model-building and inference strategies. We extend the discussion to ANCOVA's usefulness in basic 2^k factorial arrangements. Within the factorial framework, we focus on various assumptions that can be made to better manage the allocation of degrees of freedom during model estimation. Additionally, we provide a procedure to use ANCOVA with a single replicate of a factorial experiment. Examples and emphasis on computer implementation are used to illustrate the discussion throughout this tutorial.