ANALYSIS OF COVARIANCE
Measuring relevant variables for each subject before beginning an experiment can have a double benefit. One benefit is statistical: lower error variability. The other benefit is substantive: information on how the experimental effect depends on individual differences.
Consider effectiveness of different maintenance schedules on health of premature infants. We would surely measure each infant's weight at the start of the experiment. In fact, change in weight is an obvious response measure. Intuitively, the change score seems to “correct” for the initial differences in weight for different infants. But change scores are unexpectedly treacherous. Change scores should usually be avoided in favor of analysis of covariance, which extracts the help and avoids the harm.
Analysis of covariance (Ancova) rests on a simple idea. In the experiment on infant health, much of the final weight would be predictable from the initial weight. This predictable component consists of individual differences that would go into the error term in an ordinary Anova or confidence interval. But this predictable component of individual differences can be removed with regression analysis. Removing this predictable component of individual differences reduces the variability of the response, yielding tighter confidence intervals. Ancova rests on this happy marriage of Anova and regression.
Other variables could also be measured for each infant, such as birth age, a nurse's judgment of prognosis, as well as mother's health and health practices. To the extent that any such covariate correlates with infant weight gain, it also can be used to reduce error variability. The change score idea is not applicable to these other covariates, of course, but Ancova is.