A meta-analysis is a statistical process of combining multiple studies.
Introduction to meta analysis
What is meta-analysis?
Meta-analysis refers to a statistical process that compares, combines, and synthesizes research findings from multiple studies in a principled manner. Meta-analyses are largely applied to medicine and pharmacology, two of the fields on which we focus in this description.
Fixed and Random-effects models
Traditional meta-analyses, regardless of whether it is frequentist or Bayesian, aim to detect the significant difference in the effect sizes, $\delta$. Say there are $N$ studies. Then, fixed-effects meta-analyses assume the estimated effect sizes $Y_i$ for $i=1,\ldots,N$ reflect the underlying true effect $\delta$ across all $N$ studies.