Fig. 5

Different types of plots for publication bias tests: A a funnel plot using model residuals, showing a funnel (white) that shows the region of statistical non-significance (30 effect sizes from 30 studies are used; note that we used the inverse of standard errors for the y-axis, but for some effect sizes, sample size or ‘effective’ sample size may be more appropriate), B a bubble plot visualising a multilevel meta-regression that tests for the small study effect (note that the slope was non-significant: b = 0.120, 95% CI = [− 0.095, 0.334]; all effect sizes are used), and C a bubble plot visualising a multilevel meta-regression that tests for the decline effect (the slope was non-significant: b = 0.003, 95%CI = [− 0.002, 0.008])