ANCOVA versus Change Score for the Analysis of Nonexperimental Two-Wave Data: A Structural Modeling Perspective

There is an ongoing debate on whether the analysis of covariance (ANCOVA) or the change score approach is more appropriate when analyzing nonexperimental pre-post designs. In this article, we use a structural modeling perspective to clarify the different assumptions that are made by the ANCOVA and the change score approaches to identify the causal effect of a treatment variable. We show that the change score approach offers the option of controlling for unobserved confounders but relies on strong assumptions about the effects of these unobserved confounders and does not allow for dynamic causal relationships. By contrast, the ANCOVA approach is based on a selection-on-observables approach and assumes that all relevant confounders are measured. Furthermore, we illustrate conditions under which the two approaches give lower and upper bounds of the true treatment effect, and we discuss the role of measurement error. Implications for the analysis of nonexperimental two-wave data are discussed.