Analysis of covariance: Its model and use in psychological research.

Abstract
Since its development 50 years ago, the analysis of covariance (ANCOVA) has become a standard tool for data analysis in psychological research. Nevertheless, it is common for researchers to underestimate both the benefits of the technique and its potential for misuse. In this article, we consider the two major ways in which psychologists have used the technique: for increasing the precision of estimation in randomized experiments and for seeking to remove bias in nonran- domized studies. In each case, the ANCOVA is compared with analytic alternatives. The argument emphasizes the benefits of using the technique in randomized experiments and warns of the dangers of using it in nonrandomized studies. The analysis of covariance (ANCOVA) is a statistical proce- dure developed and popularized by Sir Ronald Fisher (1948) over 50 years ago. In his words, it "combines the advantages and reconciles the requirements of the two very widely appli- cable procedures known as regression and analysis of vari- ance" (Fisher, 1948, p. 281). Despite a long and distinguished history of use in data analysis and particular prominence in the social science research literature. ANCOVA remains an often misunderstood and misused technique. Fisher(1948) originally developed ANCOVA as a method for reducing error variance in randomized experiments, thereby increasing both the statistical power of hypothesis tests and the precision in estimating effects. However, social scientists have at least as frequently used the method to provide statis- tical control in nonrandomized (quasi) experiments. Perhaps the fact that ANCOVA offers these two distinctly different potential benefits—increasing precision in randomized exper- iments and reducing bias in nonrandomized studies—has contributed to confusion over its use. In our view, social scientists have underutilized the procedure for the purpose of improving the precision of estimates and overutilized it for the purpose of attempting to reduce bias in nonrandomized studies. In the following discussion, we give the statistical model for ANCOVA and then consider each of its major uses. Throughout, we make reference to potential pitfalls often found in the empirically based literature in which ANCOVA has been used. Generally, we argue for a more balanced consideration of what the procedure has to offer to psychological research. The benefits of adjustment in nonrandomized experiments are fewer than are suggested in the literature, but the need for better precision of estimates is greater.