Quality & Quantity 38: 381–389, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
CORA J. M. MAAS
, JOOP J. HOX and GERTY J. L. M.
Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht University, POB
80140, NL-3805 TC Utrecht, the Netherlands
Abstract. The goal of meta-analysis is to integrate the research results of a number of studies on a
speciﬁc topic. Characteristic for meta-analysis is that in general only the summary statistics of the
studies are used and not the original data. When the published research results to be integrated are
longitudinal, multilevel analysis can be used for the meta-analysis. We will demonstrate this with an
example of longitudinal data on the mental development of infants. We distinguish four levels in the
data. The highest level (4) is the publication, in which the results of one or more studies are published.
The third level consists of the separate studies. At this level we have knowledge about the degree of
prematurity of the group of infants in the speciﬁc study. The second level are the repeated measures.
We have data about the test age, the mental development, the corresponding standard deviations, and
the sample sizes. The lowest level is needed for the speciﬁcation of the meta-analysis model. Both
the way in which the multilevel model has to be speciﬁed (the Mln-program is used) as the results
will be presented and interpreted.
Key words: longitudinal analysis, meta-analysis, multilevel analysis.
In the social and behavioural sciences, research results are often inconsistent. Hu-
man behaviour is complex and difﬁcult to explain. Depending on characteristics of
the studies, such as samples, contextual variables and operationalizations, different
conclusions may be drawn on the same research topic. The aim of meta-analysis
(Glass, 1976; Light and Pillemer, 1984; Lipsey and Wilson, 2001) is the integration
of such different research results and the explanation of the prevailing inconsisten-
cies. Characteristic of the meta-analysis procedure is that in general only summary
statistics, as p-values, correlations or standard deviations, of the studies are used
and not the original data. So, if the research question is about the correlation
between two variables, meta-analysis is used to combine the correlations as found
in the different studies to one ‘overall correlation’. Also the deviations of the in-
dividual studies to this overall correlation are estimated. When the deviations are
Correspondence concerning this article should be sent to Cora Maas, Department of Method-
ology and Statistics, University of Utrecht, Heidelberglaan 1, 3584 CS Utrecht, The Netherlands.
Phone +31 30 2534594. Fax +31 30 253 5797. Electronic mail may be sent to email@example.com