Obtaining unbiased results in meta-analysis: the importance of correcting for statistical artefacts

Most published meta-analyses address only artefactual variance due to sampling error and ignore the role of other statistical and psychometric artefacts, such as measurement error (due to factors including unreliability of measurements, group misclassification, and variable treatment strength) and selection effects (including range restriction/enhancement and collider biases). These artefacts can have severe biasing effects on the results of individual studies and meta-analyses. Failing to account for these artefacts can lead to inaccurate conclusions about the mean effect size and between-studies effect-size heterogeneity, and can influence the results of meta-regression, publication bias, and sensitivity analyses. In this paper, we provide a brief introduction to the biasing effects of measurement error and selection effects and their relevance to a variety of research designs. We describe how to estimate the effects of these artefacts in different research designs and correct for their impacts in primary studies and meta-analyses. We consider meta-analyses of correlations, observational group differences, and experimental effects. We provide R code to implement the corrections described.