Meta-analysis as a system of springs.

Meta-analysis results are usually presented in forest plots, which show the individual study results and the summary effect along with their confidence intervals. In this paper, we propose a system of linear springs as a mechanical analogue of meta-analysis that enables visualization and enhances intuition. The length of a spring corresponds to a study treatment effect and the stiffness of the spring corresponds to its inverse variance. To synthesize study springs we use two main operations: connection in parallel and connection in series. We show the equivalence between meta-analysis and linear springs for fixed effect and random effects pairwise meta-analysis and we also derive indirect treatment effects. We use examples to illustrate the different meta-analytical schemes using the corresponding system of springs. The proposed visualization can serve as an educational tool, especially useful for researchers with no statistical background. The analogy between meta-analysis and springs facilitates intuition for notions such as heterogeneity and the differences between fixed and random effects meta-analysis.