The workbooks and a pdf-version of this user manual can be downloaded from here.
A funnel plot (see Figure 20) is a scatter plot of the studies in a meta-analysis (represented by blue dots) in a space defined by effect size (on the x-axis; scale displayed on top of the plot) and standard error (on the y-axis). It also presents the combined effect size (green dot) with its confidence interval (black) and prediction interval (green). The plot also shows a vertical line (also in red) that runs through the (adjusted) combined effect size and the corresponding lower and upper limits of the confidence interval (red diagonal lines).
The adjusted combined effect size and accompanying confidence and prediction intervals in this plot represents the results of a trim-and-fill procedure as proposed by Duval and Tweedie (2000a; 2000b).
Figure 20: Example of funnel plot part of the Publication Bias Analysis sheet
The user can turn the trim-and-fill procedure ‘On’ or ‘Off’; can decide whether to search for studies missing in the meta-analysis on the ‘Left’ or ‘Right’ side of the combined effect size; and can choose between two estimators: ‘Linear’ (also described as L0+) or ‘Leftmost / Rightmost Run’ (also described as R0+). Once the trim-and-fill is turned on, Meta-Essentials will calculate an adjusted combined effect size (with CI and PI, represented on the red horizontal line in Figure 11) as well as adjusted heterogeneity measures. These adjusted statistics are based upon the set of initially included studies expanded with the imputed data points (orange open circles in the plot, see Figure 20).
Duval, S., & Tweedie, R. (2000a). A nonparametric "trim and fill" method of accounting for publication bias in meta-analysis. Journal of the American Statistical Association, 95(449), 89-98. dx.doi.org/10.1080/01621459.2000.10473905
Duval, S., & Tweedie, R. (2000b). Trim and fill: A simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis. Biometrics, 56(2), 455-463. dx.doi.org/10.1111/j.0006-341x.2000.00455.x