Forest Plot

A forest plot is a type of graphical display most frequently used in systematic reviews and meta-analyses. The purpose of a forest plot is to summarize and facilitate visual interpretation of findings from individual studies. This entry presents brief descriptions of meta-analysis and forest plot and discusses the interpretation of forest plots, both numerical results and visual demonstration.

Meta-analysis is a statistical procedure that aggregates data from multiple studies to estimate the overall effect size and quantify excess variability around the effect size (variability beyond what would be expected from sampling error). By combining results from across studies and numbers of study participants, it maximizes power and precision. The effect sizes from each study may be summarized using a forest plot. Risk ratios and odds ratios are often used as effect sizes for dichotomous data, and mean differences, standardized mean differences, Hedges’ g, or correlations are commonly used for continuous data.

Forest plots present one row for each effect size and a final row for the weighted mean effect size. Rows can be ordered in several ways, but usually the most useful is by the magnitude of the effect. If the effect sizes can be nested within a potential moderator variable, the rows can be ordered by effect size within values of that moderator variable: for example, first for studies conducted in science classrooms and second for studies conducted in English language arts classrooms.

Multiple columns are presented with critical information about each effect size. Columns typically fall into four categories: (1) study identification, (2) effect size information, (3) important meta-data about each effect size, and (4) graphical presentation of the effect size and its confidence interval. Usually the first column provides a name for the individual study or subgroup details—often this is the author name, perhaps followed by the year the study was published.

Effect size information consists of the effect size, the lower and upper limits of the (typically .95) confidence interval around that effect size, and perhaps the p value associated with the effect size. Frequently, the effect size is presented as an odds ratio or risk ratio if the outcomes are binary or as a standardized mean difference or correlation if the outcomes are continuous. Many other types of effect sizes are possible.

[Page 590]Meta-data about effect sizes usually describe the sample or study procedures. Frequently the sample sizes of the control and treatment groups and/or the weight that will be applied to each effect size to calculate the weighted mean effect size that summarizes the studies are presented. Depending on the set of studies available, meta-data might describe the demographics of the sample (e.g., urban, suburban, rural; male, female; science classrooms, mathematics classrooms, English language arts classrooms) or the research design (e.g., random assignment, matched groups, naturally occurring groups). These study and research design descriptors might also serve to order the rows of effect sizes.

The heart of the forest plot is the graphical display of the effect size confidence interval. As can be seen in Figure 1, which is based on fake data and produced by the R Meta package at the bottom of this column the scale is provided for the effect sizes. In the case of odds ratios and risk ratios, it might be presented logarithmically (e.g., equally spacing .01, .1, 1, 10, and 100) or, especially in case of standardized mean differences, linearly (e.g., −2. −1, 0, 1, 2). Vertical lines indicate key values of the effect size scale. A particularly important vertical indicator is the “line of no effect” or “line of no difference.” The line of no effect intersects the horizontally displayed confidence intervals around each effect size and represents where the intervention had no effect. If the statistical technique used in the meta-analysis is risk ratio or odds ratio, this line of no effect would be 1. That means the intervention produces an effect size equal to the control group, thus the numerator and denominator in the ratio are the same, and the ratio is 1. If the technique used is a standardized mean difference, the line of no effect would be 0. Indicator of scale (the number at the line of no effect) and direction of effect are labeled at the bottom of the forest plot.

...