A meta-analysis involves the process of fitting one or multiple statistical models to a collection of effect sizes or observed outcomes. Commonly used meta-analytic models make various assumptions, including normality of the sampling distributions, unbiasedness of the estimates, known sampling variances, and the absence of correlation between the sampling errors and the random effects. In this chapter, we thoroughly review these assumptions and examine methods to check for their violation. Moreover, methods for assessing the model fit, testing for model misspecification, and checking for the presence of outliers and influential studies are described. Many of the methods and diagnostic plots discussed rely on so-called deletion diagnostics, where one or multiple studies are deleted from the dataset and changes in various aspects of the fitted models are examined.
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