Confidence interval estimation for standardized effect sizes in multilevel and latent growth modeling.

OBJECTIVE: Multilevel and latent growth models are frequently used interchangeably to examine differences between groups in trajectories of outcomes from controlled clinical trials. The unstandardized coefficient for the effect from group to slope (the treatment effect) from such models can be converted to a standardized mean difference (Cohen's d) between the treatment and control groups at end of study. This article addresses the confidence interval (CI) for this effect size. METHOD: Two sets of equations for estimating the CI for the treatment effect size in multilevel models were derived, and the usage of each was illustrated with data from the National Youth Study (Elliott, Huizinga, & Menard, 1989). Validity of the CIs was examined with a Monte Carlo simulation study that manipulated effect potency and sample size. RESULTS: The equivalence of the 2 new CI estimation methods was demonstrated, and the Monte Carlo study found that bias in the CI for the effect size was not appreciably larger than bias in the CI for the widely used unstandardized coefficient. CONCLUSIONS: Investigators reporting this increasingly popular effect size can estimate its CI with equations presented in this article.