The Use of Analysis of Covariance in Tests of Attribute-by-Treatment Interactions

Abstract

The use of analysis of covariance (ANCOVA) is examined for attribute-by-treatment interaction (ATI) research, where participants are randomly assigned to treatments but not to levels of the attribute factor. A survey of the ATI literature revealed that ANCOVA was typically not used and was some-times misunderstood. The current paper demonstrates that, contrary to what some have thought, the use of a covariate does not confound the interpretation of the interaction between attribute and treatment, because the expected value of the interaction effect is independent of the particular covariate chosen. Independence occurs regardless of (1) whether the covariate is measured with perfect or less than perfect reliability, (2) whether the attribute variable is discrete or continuous, and (3) whether sample sizes are equal or proportional. The primary implication of these results is that ANCOVA provides a needed means for researchers to achieve powerful designs for assessing ATI's.