Funnel Plots

We know Publication Bias exists. Journals prefer positive results. Negative results stay in the drawer.

But how do we prove something is missing?

We use a Funnel Plot.

The Concept

In a meta-analysis, we plot every study on a graph.

• X-axis: The result (Effect Size).
• Y-axis: The precision (Sample Size).

Big studies (high precision) should be close to the true average. They sit at the top. Small studies (low precision) bounce around randomly. They spread out at the bottom.

Ideally, this forms a symmetrical upside-down funnel (or triangle).

The Bite Out of the Apple

If there is publication bias, the funnel looks weird.

Small studies that show negative results are missing. They were never published. So, the bottom corner of the funnel is empty. It looks like someone took a bite out of the triangle.

The Diagnosis

When you look at a meta-analysis, always check the funnel plot.

If it is asymmetrical, the meta-analysis is likely overestimating the benefit. The "truth" is hidden in the empty space.