In this article, three multilevel models for meta-analysis are examined. Hedges and Olkin suggested that effect sizes follow a noncentral t distribution and proposed several approximate methods. Raudenbush and Bryk further refined this model; however, this procedure is based on a normal approximation. In the current research literature, this approximate procedure has not been compared to one based directly on the noncentral t distribution, which is the approach taken in this article. A multilevel model is presented, and estimation is carried out on a real data set using the Markov chain Monte Carlo (MCMC) procedure. A simulation study is then conducted to examine the properties of the noncentral t approach in more depth. Finally, an example of code written in WinBUGS is given, which may be useful to researchers across a broad range of disciplines.
All Science Journal Classification (ASJC) codes
- Social Sciences (miscellaneous)
- MCMC estimation
- Multilevel analysis
- Noncentral t distribution
- Psychotherapy outcomes