On the Relationship between ANOVA Main Effects and Average Treatment Effects

In unbalanced designs, there is a controversy about which ANOVA type of sums of squares should be used for testing main effects and whether main effects should be considered at all in the presence of interactions. Looking at this problem from a causal inference perspective, we show in which designs and under which conditions the ANOVA main effects correspond to average treatment effects as defined in the causal inference literature. We consider balanced, proportional and nonorthogonal designs, and models with and without interactions. In balanced designs, main effects obtained by type I, II, and III sums of squares all correspond to the average treatment effect. This is also true for proportional designs except for ANOVA type III which leads to bias if there are interactions. In nonorthogonal designs, ANOVA type I is always highly biased and ANOVA type II and III are biased if there are interactions. In a simulation study, we confirm our theoretical results and examine the severity of bias under different conditions.

Efficient Experimental Design with Marketing Research Applications

The authors suggest the use of D-efficient experimental designs for conjoint and discrete-choice studies, discussing orthogonal arrays, nonorthogonal designs, relative efficiency, and nonorthogonal design algorithms. They construct designs for a choice study with asymmetry and interactions and for a conjoint study with blocks and aggregate interactions.

Nonorthogonal Analysis of Variance Programs: An Evaluation

Recently, at least four methods have been suggested for the analysis of nonorthogonal designs. However, even researchers who have decided which method is appropriate often do not know which computer programs are capable of performing the desired analysis. In addition, available programs differ widely in their accuracy and ease of use. We have evaluated some widely used ANOVA computer programs with respect to their capabilities for performing analyses using all four methods, their accuracy in performing these analyses, and other characteristics which influence their utility.