Things to Know:

Analysis of Covariance (ANCOVA)
Analysis of Covariance is not necessarily a repeated measure design but it does use regression techniques. The basic idea is that there is a covariate or set of covariates. These are variables that are correlated with your DV. Perhaps the effect of these covariates should be removed before you test the difference between experimental conditions.

For example, if your ANOVA has four groups being tested on how different teaching methods influence arithmetic scores and your groups differ in IQ, the IQ differences would interfere with analyzing the effects of teaching method. Would the scores just reflect the basic ability differences in the groups and not the methods?

You, thus, can correlate the IQ variable with the arithmetic scores. If there is a significant correlation, you can predict the arithmetic scores from IQ. In an ANCOVA design, we will then compute the predicted arithmetic Score. We would subtract the predicted score from the original arithmetic score.

This difference or residual score (Arithmetic - Arith. pred) would then be the actual score used for an ANOVA. Such an ANOVA is an ANCOVA. So, an ANCOVA is just an ANOVA run on the residuals after predictions of the DV have been made from a set of covariates. It is also the case that an appropriate ANCOVA design will increase statistical power, as the analysis based on residuals will have smaller error terms.