Publication bias in research synthesis: Sensitivity analysis using a priori weight functions

Publication bias, sometimes known as the file-drawer problem or funnel-plot asymmetry, is common in empirical research. The authors review the implications of publication bias for quantitative research synthesis (meta-analysis) and describe existing techniques for detecting and correcting it. A new approach is proposed that is suitable for application to meta-analytic data sets that are too small for the application of existing methods. The model estimates parameters relevant to fixed-effects, mixed-effects or random-effects meta-analysis contingent on a hypothetical pattern of bias that is fixed independently of the data. The authors illustrate this approach for sensitivity analysis using 3 data sets adapted from a commonly cited reference work on research synthesis (H. M. Cooper & L. V. Hedges, 1994).