Publication bias and the funnel shape
A funnel plot displays the results of multiple studies in a meta-analysis, with effect size on the horizontal axis and study precision (inverse standard error) on the vertical axis. Studies are scattered as points. In the absence of bias, studies form a symmetric funnel: large, precise studies cluster near the true effect at the top; smaller, noisier studies spread wider. Asymmetry in the funnel (missing studies on one side) suggests publication bias: smaller studies with unfavorable results were never published, leaving only larger studies and favorable small studies, which distorts the average effect estimate.
Interpretation and adjustment strategies
A symmetrical funnel increases confidence that the meta-analysis result is not biased. A noticeably asymmetrical funnel warrants further investigation: heterogeneous study quality (some studies are more rigorous than others), outcome reporting bias, or true publication bias. Visual inspection of the funnel is informal; formal tests like Egger regression quantify asymmetry. If bias is suspected, sensitivity analyses (e.g., removing small studies or trimming the extremes) test robustness. Some analysts apply trim-and-fill methods to estimate what unpublished studies might say.