# Meta-analysis

A meta-analysis is a statistical practice of combining the results of a number of studies that address a set of related research hypotheses. The first meta-analysis was performed by Karl Pearson in 1904, in an attempt to overcome the problem of reduced statistical power in studies with small sample sizes; analyzing the results from a group of studies can allow more accurate estimation of effects.

Meta-analysis is a collection of systematic techniques for resolving apparent contradictions in research findings. Meta-analysts translate results from different studies to a common metric and statistically explore relations between study characteristics and findings.

Although meta-analysis is widely used in evidence-based medicine today, a meta-analysis of a medical treatment was not published till 1955. In the 1970s more sophisticated analytical techniques were introduced in educational research, starting with the work of Gene V Glass. The online Oxford English Dictionary lists the first usage of the term in the statistical sense as 1976 by Glass. The statistical theory surrounding meta-analysis was greatly advanced by the work of Larry V. Hedges and Ingram Olkin.

Because the results from different studies investigating different dependent variables are measured on different scales, the dependent variable in a meta-analysis is some standard measure of effect size. To describe the results of comparative experiments the usual effect size indicator is the standardized mean difference (d) which is the standard score equivalent to the difference between means, or an odds ratio if the outcome of the experiments is a dichotomous variable (success versus failure). A meta-analysis can be performed on studies that describe their findings in correlation coefficients, as for example, studies of the familiar relationship of intelligence. In these cases, the correlation itself is the indicator of the effect size. Nor is the method restricted to situations in which one or more variables is properly referred to as "dependent." For example, a meta-analysis could be performed on a collection of studies each of which attempts to estimate the incidence of left-handedness in various groups of people.

Modern meta-analysis does more than just combine the effect sizes of a set of studies. It tests if the studies' outcomes show more variation than the variation that is expected because of sampling different research participants. If that is the case, study characteristics such as measurement instrument used, population sampled, or aspects of the studies' design are coded. These characteristics are then used as predictor variables to analyze the excess variation in the effect sizes.

A weakness of the method is that sources of bias are not controlled by the method. A good meta-analysis of badly designed studies will still result in bad statistics. Robert Slavin has argued that only methodologically sound studies should be included in a meta-analysis, a practice he calls 'best evidence meta-analysis'. Other meta-analysts would include weaker studies, and add a study-level predictor variable that reflects the methodological quality of the studies to examine the effect of study quality on the effect size.

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