Insyt
All charts in the library

Uncertainty and models

Funnel plot (meta-analysis)

Plots study effects against precision or standard error to inspect small-study patterns.

  • Plot
  • Model diagnostics
  • Small-study-effect assessment

What it answers

Are smaller or less precise studies distributed asymmetrically?

Shape
Effect points in a funnel-shaped envelope
What it shows
Small-study patterns and outliers.

Example

The question

Which stores have unusual return rates, allowing for their size?

Return rate against number of orders, 40 stores, with expected range (funnel plot)

Return rate against number of orders, 40 stores, with expected range (funnel plot)Each dot is a store; dashed curves mark the range expected by chance around the 8% average, wider for small stores. Two stores sit outside the outer curve: one large store at 11.5% and one small store at 2.5%.Return rate (%)048121601,0002,0003,000Orders in the year
Return rate against number of orders, 40 stores, with expected range (funnel plot)Each dot is a store; dashed curves mark the range expected by chance around the 8% average, wider for small stores. Two stores sit outside the outer curve: one large store at 11.5% and one small store at 2.5%.Return rate (%)048121601,0002,0003,000Orders in the year
Each dot is a store; dashed curves mark the range expected by chance around the 8% average, wider for small stores. Two stores sit outside the outer curve: one large store at 11.5% and one small store at 2.5%.

Illustrative data. It belongs to no company.

When to use it

Use it when

Exploratory meta-analysis diagnostics.

Avoid it when

Very few studies or treating asymmetry as proof of publication bias.

How to read it

Read effect against standard error/precision and interpret the envelope convention.

Note

Asymmetry alone does not prove publication bias.

The data you need

Layout
Long table
Fields
StudyID: text; EffectEstimate: number; StandardError: positive number
One row is
One study effect and its standard error. What is the grain?
Rules
Use a common effect scale and define the vertical axis as standard error or a specified precision transformation.
Optional
SampleSize can support alternative funnel conventions but is not interchangeable with standard error.
Preparation
Fit or obtain a suitable model/estimate first, then pair estimates with correctly labelled bounds or standard errors. Preserve coverage and scale information.
Units
X uses a common effect scale; Y uses standard error or specified precision. No business stage-conversion denominator.
Example of the input layout: Long tableA long table: one row per observation, few columns. New data adds rows.StudyIDEffectEstimStandardErrAABBC
A long table: one row per observation, few columns. New data adds rows.

Worked example

StudyA effect 0.20, SE0.05; B0.10, SE0.12. A ismore precise. Two studies are far too few to assess funnel asymmetry.

StudyIDEffectEstimateStandardError
A0.200.05
B0.100.12
C0.250.08
All charts in the library