are useful adjuncts to meta-analyses. A funnel plot is a [[scatterplot]] of treatment effect against a measure of study sizeprecision. It is used primarily as a visual aid for detecting bias or [[Study heterogeneity|systematic heterogeneity]]. A [[Symmetry|symmetric]] inverted funnel shape arises from a ‘well-behaved’ data set, in which publication bias is unlikely. An asymmetric funnel indicates a relationship between treatment effect estimate and study sizeprecision. This suggests the possibility of either [[publication bias]] or a systematic difference between smallerstudies of higher and largerlower studiesprecision (typically ‘small study effects’). Asymmetry can also arise from use of an inappropriate effect measure. Whatever the cause, an asymmetric funnel plot leads to doubts over the appropriateness of a simple meta-analysis and suggests that there needs to be investigation of possible causes.
A variety of choices of measures of ‘study size’precision’ is available, including total sample size, [[Standard error (statistics)|standard error]] of the treatment effect, and inverse [[variance]] of the treatment effect ([[Weight function|weight]]). Sterne and Egger have compared these with others, and conclude that the standard error is to be recommended.<ref name="SterneJ2001Funnel"/>
When the standard error is used, straight lines may be drawn to define a region within which 95% of points might lie in the absence of both [[Heterogeneous|heterogeneity]] and publication bias.<ref name="SterneJ2001Funnel"/>
In common with [[confidence interval]] plots, funnel plots are conventionally drawn with the treatment effect measure on the [[Cartesian coordinate system|horizontal axis]], so that study sizeprecision appears on the vertical axis, breaking with the general rule. Since funnel plots are principally visual aids for detecting asymmetry along the treatment effect axis, this makes them considerably easier to interpret.
