Multiplicative Treatment Effects in Randomized Pretest-posttest Experimental Designs

In randomized pretest-posttest experimental designs, experimental treatments are commonly compared through an additive difference. The assumed additive effects of experimental treatments, in randomized pretest-posttest design, also correspond to additive differences between pre- and posttreatment measures. However, it is possible that experimental treatments differ in ratios and the treatment effects are multiplicative. Logarithmic-transformed ANOVA (LANOVA) and logarithmic-transformed ANCOVA (LANCOVA)-reparameterizations of log-log regression models-are proposed to test multiplicative effects given randomized pretest-posttest experimental designs. In addition, a new effect size measure is proposed for treatment effects that are multiplicative instead of additive. Model selection strategy, sample size planning, and power calculation for the proposed methods are also provided. Simulation studies were conducted to compare the Type I error rates and power of proposed methods to those of symmetrized change analysis, ANOVA, ANCOVA, gain score analysis, and ANCOVA with logarithmic-transformed dependent variable given population effect of both additive and multiplicative nature. An empirical data analysis follows to show the interpretational difference between multiplicative and additive effects. While logarithmic transformations are most often recommended to address skewness, our article shows how a log transformation can be used to reconceptualize the fundamental nature of the treatment effect. Finally, recommendations, limitations, and future directions are discussed. (PsycINFO Database Record (c) 2020 APA, all rights reserved).