Solution: Analysis of Covariance (ANCOVA)
UseGENERAL LINEAR MODELS (GLM) or GENERAL ANOVA/MANOVA. These chapters discuss techniques to perform analyses with one or more covariates, and to test for parallelism of regression lines/planes in different groups.
Usually, the purpose of analysis of variance (ANOVA) is to compare means between different groups/samples or variables/measurements. In analysis of covariance (ANCOVA), one can simultaneously perform a regression analysis, that is, evaluate the relationship between one or more independent or predictor variables (also called covariates) with the dependent variable(s). For example, we may have two different methods for teaching math that were used in two different classes (groups/samples). In addition to final math ability, we may have collected data on general intelligence. It would be of interest to see, whether the relationship between general intelligence and math ability is stronger or weaker, depending on the teaching method.
In ANCOVA terminology, this hypothesis refers to the parallelism of the regression lines in the two classes. If those lines are parallel, then the relationship in the two classes is the same, and thus the relationship between intelligence and math ability is not moderated by the teaching method. If they are not parallel, we conclude that the teaching method does, in fact, moderate that relationship.