Figure 2. Step-wise illustration of distortion in SMD versus SE funnel plots.

(A) Depicted are simulated studies with a sample size of respectively 10 (large black circles), 25 (blue squares), 50 (red triangles), 100 (small green circles) and 200 (gold asterisks) subjects per group, and an SMD of zero. The SE of these studies (indicated by the dashed line for studies with n = 10) solely depends on their sample size, as SMD² = 0 and therefore does not contribute to the equation for the SE. As expected, the SE decreases as the sample size increases. (B) Five data points from simulated studies with n = 10 and a stepwise increasing SMD are added to the plot. For these studies, the SMD² contributes to the equation for the SE, and the SE will decrease even though the sample size is constant. The dotted line represents a hypothetical summary effect of SMD = 1 in a meta-analysis. Note that when assessing a funnel plot for asymmetry around this axis, the data points with an SMD < 1 have skewed to the upper left-hand region, whereas studies with an SMD > 1 are in the lower right region of the plot. This distortion worsens as the SMD increases. (C) Because the SMD is squared in the equation for the SE, the same distortion pattern is observed for negative SMDs. Thus, funnel plots will be distorted most when the study samples sizes are small and SMDs are either very positive or very negative. (D) The same deviation is observed for simulated studies with larger sample sizes, however, the deviation decreases as the sample size increases, because the sample size will outweigh the effect of SMD² in the equation for the SE.