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The funnel plot is a graphical visualisation of summary data estimates from ameta-analysis, and is a useful tool for detecting departures from the standardmodelling assumptions. Although perhaps not widely appreciated, a simpleextension of the funnel plot can help to facilitate an intuitive interpretationof the mathematics underlying a meta-analysis at a more fundamental level, byequating it to determining the centre of mass of a physical system. We usedthis analogy, with some success, to explain the concepts of weighing evidenceand of biased evidence to a young audience at the Cambridge Science Festival,without recourse to precise definitions or statistical formulae. In this paperwe aim to formalise this analogy at a more technical level using the estimatingequation framework: firstly, to help elucidate some of the basic statisticalmodels employed in a meta-analysis and secondly, to forge new connectionsbetween bias adjustment in the evidence synthesis and causal inferenceliteratures.

On the physical interpretation of a meta-analysis in the presence of heterogeneity and bias: from clinical trials to Mendelian randomization