Random-effects meta-analysis is the statistical synthesis of trials that examine the same or similar research question under the assumption that the underlying true effects differ across trials. The notion of true effect refers to the unobserved effect that each trial aims to estimate and would observe if it had infinite sample size. While in the fixed-effect analysis it is deemed possible that the true effect is a single value, common across all trials, this assumption is relaxed in the random-effects analysis. Concretely, when the random-effects analysis is adopted, the researcher assumes that the true underlying effects are different yet related across studies. The relation between true effects is expressed by a normal distribution that the true effects are assumed to follow.
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