The misuse of ANCOVA in neuroimaging studies

Analysis of Covariance (ANCOVA) is a technique that is frequently used in neuroimaging studies to control for covariates. An assumption of ANCOVA is that the between-subjects factor and the covariate are independent. In some observational studies in the neuroimaging literature, this assumption is violated. The question that these studies attempt to answer is what the difference would be between group means on the dependent variable if the group means on the covariate were equal. However, when there is a dependency between the between-subjects factor and the covariate, then correcting for differences between groups on the covariate may misrepresent the factor and distort its definition. Moreover, the situation where all subjects have equal scores on the covariate may be unrealistic. If the assumption of independence is violated, there are several procedures to follow. Generally, it is of crucial importance to consider the question what it means to correct for a variable that has a relationship with the factor under study. In case of an observational study, ANCOVA does not facilitate the estimation of the causal effect of the between-subjects factor. When two variables are related, there is no statistical method available to correct for this relationship.