The analysis of covariance: a useful technique for analysing quality improvement experiments

• Published in: Quality and reliability engineering international Vol. 15; no. 4; pp. 303 - 316
• Main Authors: Silknitter, Kevin O., Wisnowski, James W., Montgomery, Douglas C.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.07.1999; Wiley
• Subjects: analysis of covariance; Applied sciences; Computer science; control theory; systems; Computers in experimental physics; Control theory. Systems; Design of experiments; design process; Exact sciences and technology; factorial design; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Modelling and identification; Physics; regression modelling; Model matching; Covariance; Experimental design; Regression analysis; System identification; Measurement method; Experimental study; Factorial design
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/(SICI)1099-1638(199907/08)15:4<303::AID-QRE253>3.0.CO;2-G

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 2k 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. Copyright © 1999 John Wiley & Sons, Ltd.