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Research conclusions in the social sciences are increasingly based on meta-analysis, making questions of the accuracy of meta-analysis critical to the integrity of the base of cumulative knowledge. Both fixed effects (FE) and random effects (RE) meta-analysis models have been used widely in published meta-analyses. This article shows that FE models typically manifest a substantial Type I bias in significance tests for mean effect sizes and for moderator variables (interactions), while RE models do not. Likewise, FE models, but not RE models, yield confidence intervals for mean effect sizes that are narrower than their nominal width, thereby overstating the degree of precision in meta-analysis findings. This article demonstrates analytically that these biases in FE procedures are large enough to create serious distortions in conclusions about cumulative knowledge in the research literature. We therefore recommend that RE methods routinely be employed in meta-analysis in preference to FE methods.