Standardized Mean Difference for Three-Level Partially Nested Data

• In Event: 66.052 - Estimation Accuracy and Conditions for Complex Multilevel Models

Abstract

We propose two approaches for obtaining standardized mean difference effect size and the
corresponding sampling variance for partially nested data with a three-level treatment arm and an unclustered control arm. The first estimator, denoted as d (dW with pooled SD and dC with
control arm SD), requires input of summary statistics and is useful for meta-analyses and
secondary data analyses; the second estimator δ( δW and δC ) takes parameter estimates from a
multilevel model as input and is mainly of interest to researchers doing primary research.
Simulation results showed that the two methods (d and δ) produced unbiased point and variance
estimates for effect size. We also illustrate the procedures using a hypothetical example of therapy groups clustered within therapists.

Authors

• Hok Chio (Mark) Lai, University of Cincinnati

• Oiman Kwok, Texas A&M University - College Station