In this article, the authors compare the multilevel meta-analysis approach with the more traditional meta-analytical approaches. After a description and comparison of the underlying models and some of the major techniques, the results of the multilevel approach are compared with those of the traditional approaches, using a simulation study. The results of the simulation study suggest that the maximum likelihood multilevel approach is in general superior to the fixed-effects approaches, unless only a small number of studies is available. For models without moderators, the results of the multilevel approach, however, are not substantially different from the results of the traditional random-effects approaches.Meta-analyses were performed even long before Glass (1976) introduced the term meta-analysis to refer to "the statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings" (p. 3). Rosenthal (1961) was one of the first behavioral scientists who systematically combined the results of several studies, but most of the techniques that were used by Rosenthal or others are based on techniques that were developed in the beginning of the 20th century (Olkin, 1990).A real breakthrough of meta-analysis came with the presentation and implementation of a set of meta-analytic techniques presented by Glass and his colleagues (Glass, 1976(Glass, , 1977Glass, MacGaw, & Smith, 1981; Smith & Glass, 1977). Whereas in previous meta-analyses p values typically were combined, Glass (1976) emphasized the use of effect sizes. Results from different studies were summarized by calculating the mean and standard devia-

To investigate the generalizability of the results of single-case experimental studies, evaluating the effect of one or more treatments, in applied research various simultaneous and sequential replication strategies are used. We discuss one approach for aggregating the results for single-cases: the use of hierarchical linear models. This approach has the potential to allow making improved inferences about the effects for the individual cases, but also to estimate and test the overall effect, and explore the generality of this effect across cases and under different conditions.

No abstract

No abstract