A scatter that reveals what a literature is missing

A funnel plot puts each study's effect estimate on one axis and its precision on the other.

Effect against precision

A funnel plot puts each study's effect estimate on one axis and its precision on the other. Precise studies cluster near the centre, imprecise ones scatter widely, and the expected shape is a symmetric inverted funnel.

Asymmetry suggests absence

If small studies appear only on one side, small studies on the other side are probably missing. The commonest explanation is that small null or unfavourable results were never published, which is the bias the plot is used to detect.

It is a prompt, not a proof

Asymmetry has causes other than publication bias, including genuine differences between small and large studies in how they were conducted. The plot identifies something to explain rather than establishing what it is.

It needs enough studies

With fewer than about ten studies the shape is uninterpretable and the associated statistical tests have almost no power. Funnel plots presented for a handful of studies are decoration.

Choice of axis matters

Different precision measures produce different-looking plots from identical data, and the choice can create or hide apparent asymmetry. Papers should state which was used, and many do not.

Trim-and-fill estimates the missing

A related method imputes the studies that would restore symmetry and recalculates the pooled effect. The adjusted figure is a thought experiment rather than a measurement, and treating it as the corrected answer overstates it.

Registries are the better instrument

Comparing trial registrations against publications identifies missing studies directly rather than inferring them from a shape. Where a registry exists, that comparison is far stronger evidence.

What to take from one

Whether a review looked for the problem at all. A review that presents a funnel plot and discusses it is more trustworthy than one that neither plots nor mentions it, almost regardless of what the plot shows.

Small-study effects have innocent causes

Small trials are often conducted in narrower populations with tighter protocols, which can genuinely produce larger effects than broad multi-centre work. Asymmetry is therefore consistent with real differences in how small and large studies are run, and attributing it automatically to suppressed results overstates what the plot shows.

Why ten studies is the usual floor

With fewer, the scatter is dominated by chance and any apparent shape is unreliable. Statistical tests for asymmetry have very low power at small numbers, so a non-significant test in a small review is close to uninformative rather than reassuring.

Where to check this independently

The claims on this page about a scatter that reveals what a literature is missing can be checked against sources outside this site:

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