ABSTRACT

Analysis of covariance (ANCOVA) is another variant of analysis of variance in which the analyst enters into the analysis a variable(s) other than the dependent variable on which participants are also measured, called a covariate. ANCOVA has two major advantages over ANOVA. First, it provides a way to statistically equate groups that have somewhat different values on the covariate. Second, and most important, using the covariate can reduce unexplained variability, thereby increasing power to detect an effect of the independent variable. Additionally, not adjusting for a covariate may lead to the wrong conclusions. Specifically, random assignment does not guarantee that the groups are the same on the dependent variable before the experiment begins. If you are studying ways to decrease depression, for example, you may have a group of participants that were more depressed to begin with than the other groups. If you do not covary out pretest depression, it will look like there was not a treatment effect at the end of the experiment even if the treatment was efficacious, because their scores were already higher than everyone else’s. In ANCOVA, a participant’s response on the dependent variable is adjusted for the value of the covariate by calculating what that response would have been if all participants had had the same value for the covariate. Subsequent aspects of the analysis then use this adjusted dependent variable. Removing the covariate error variance from both the denominator and numerator of the F ratio generally increases the F ratio, making for a more powerful F test.