The presence of random error may be an under-recognised source of spurious findings in meta-analyses. Sample size requirements for a conclusive meta-analysis should be no less rigorous than for a single clinical trial. Meta-analyses conducted before reaching a sufficient sample size should account for the increased risk of random error. We analysed 33 meta-analyses with a sufficient sample size to detect a realistic treatment effect. We evaluated statistical significance using two-sided O’Brien-Fleming monitoring boundaries and the conventional criterion (p<0.05). Interim false positive conventional significance and clinically important overestimates of treatment effects were observed one third of the meta-analyses. The monitoring boundaries eliminated all spurious findings. Sample size requirements and monitoring boundaries may help control the risk of random errors in meta-analyses.