Randomized pretest-posttest experimental designs are often used in psychology to examine treatment effects. Common statistical methods for assessing treatment effects typically assume that both the treatment effect and the change from pre- to posttreatment are additive. However, in some circumstances, both the treatment effect and the change from pre to post can actually be multiplicative. For example, a treatment for depression, instead of incurring a constant decrease for everyone, can induce a ratio-wise shrinkage in symptom scores. That is, the treatment can result in greater improvement in depression symptoms for those with higher pretreatment depression level. We propose logarithmic-transformed ANOVA (LANOVA) and logarithmic-transformed ANCOVA (LANCOVA) to test multiplicative effects in randomized pretest-posttest experimental designs. We provide theoretical and methodological guidance to help researchers determine when it would be appropriate to apply our proposed models. We showed the efficacy of our proposed models in simulation studies and illustrated the utility of our proposed models and model selection methods in an empirical data demonstration. We also propose a new effect size measure to help researchers describe and interpret between-groups multiplicative effects. Power analysis and sample size planning for the proposed methods are discussed. In addition, we offer software implementations of our methods. We hope to encourage researchers to consider the fundamental nature of their treatment effects and to consider testing and estimating multiplicative treatment effects.

Lab documents for Quantitative Methods 2 (Spring 2019) at University of Notre Dame