Abstract. The funnel plot is widely used in meta-analyses to assess potential publication bias. However, experimental evidence suggests that informal, mere visual, inspection of funnel plots is frequently prone to incorrect conclusions, and formal statistical tests (Egger regression and others) entirely focus on funnel plot asymmetry. We suggest using the visual inference framework with funnel plots routinely, including for didactic purposes. In this framework, the type I error is controlled by design, while the explorative, holistic, and open nature of visual graph inspection is preserved. Specifically, the funnel plot of the actually observed data is presented simultaneously, in a lineup, with null funnel plots showing data simulated under the null hypothesis. Only when the real data funnel plot is identifiable from all the funnel plots presented, funnel plot-based conclusions might be warranted. Software to implement visual funnel plot inference is provided via a tailored R function.

Abstract. Currently, dedicated graphical displays to depict study-level statistical power in the context of meta-analysis are unavailable. Here, we introduce the sunset (power-enhanced) funnel plot to visualize this relevant information for assessing the credibility, or evidential value, of a set of studies. The sunset funnel plot highlights the statistical power of primary studies to detect an underlying true effect of interest in the well-known funnel display with color-coded power regions and a second power axis. This graphical display allows meta-analysts to incorporate power considerations into classic funnel plot assessments of small-study effects. Nominally significant, but low-powered, studies might be seen as less credible and as more likely being affected by selective reporting. We exemplify the application of the sunset funnel plot with two published meta-analyses from medicine and psychology. Software to create this variation of the funnel plot is provided via a tailored R function. In conclusion, the sunset (power-enhanced) funnel plot is a novel and useful graphical display to critically examine and to present study-level power in the context of meta-analysis.

Abstract. Which data to analyze, and how, are fundamental questions of all empirical research. As there are always numerous flexibilities in data-analytic decisions (a “garden of forking paths”), this poses perennial problems to all empirical research. Specification-curve analysis and multiverse analysis have recently been proposed as solutions to these issues. Building on the structural analogies between primary data analysis and meta-analysis, we transform and adapt these approaches to the meta-analytic level, in tandem with combinatorial meta-analysis. We explain the rationale of this idea, suggest descriptive and inferential statistical procedures, as well as graphical displays, provide code for meta-analytic practitioners to generate and use these, and present a fully worked real example from digit ratio (2D:4D) research, totaling 1,592 meta-analytic specifications. Specification-curve and multiverse meta-analysis holds promise to resolve conflicting meta-analyses, contested evidence, controversial empirical literatures, and polarized research, and to mitigate the associated detrimental effects of these phenomena on research progress.

Background: Data-visualization methods are essential to explore and communicate meta-analytic data and results. With a large number of novel graphs proposed quite recently, a comprehensive, up-to-date overview of available graphing options for meta-analysis is unavailable. Methods: We applied a multi-tiered search strategy to find the meta-analytic graphs proposed and introduced so far. We checked more than 150 retrievable textbooks on research synthesis methodology cover to cover, six different software programs regularly used for meta-analysis, and the entire content of two leading journals on research synthesis. In addition, we conducted Google Scholar and Google image searches and cited-reference searches of prior reviews of the topic. Retrieved graphs were categorized into a taxonomy encompassing 11 main classes, evaluated according to 24 graph-functionality features, and individually presented and described with explanatory vignettes. Results: We ascertained more than 200 different graphs and graph variants used to visualize meta-analytic data. One half of these have accrued within the past 10 years alone. The most prevalent classes were graphs for network meta-analysis (45 displays), graphs showing combined effect(s) only (26), funnel plot-like displays (24), displays showing more than one outcome per study (19), robustness, outlier and influence diagnostics (15), study selection and p-value based displays (15), and forest plot-like displays (14). The majority of graphs (130, 62.5%) possessed a unique combination of graph features. Conclusions: The rich and diverse set of available meta-analytic graphs offers a variety of options to display many different aspects of meta-analyses. This comprehensive overview of available graphs allows researchers to make better-informed decisions on which graphs suit their needs and therefore facilitates using the meta-analytic tool kit of graphs to its full potential. It also constitutes a roadmap for a goal-driven development of further graphical displays for research synthesis.

No abstract