chapter  7
26 Pages

Meta-Analysis 1: Introduction and Forest Plots

Meta-analysis can produce strong evidence where at first sight there seems to be only weak evidence. It can turn long CIs into short ones (well, sort of), find answers in what looks like a mess, and settle heated controversies. Much of what it does can be revealed in a beautiful picture called a forest plot. In this chapter I’ll discuss forest plots and explain why I think meta-analysis and meta-analytic thinking are so great. Then in Chapter 8 there’s more about ESCI and the two most important meta-analysis models. Chapter 9 outlines how to conduct a large meta-analysis and describes even more meta-analysis goodies. At La Trobe University our large classes of beginning psychology stu-

dents have for years used ESCI forest plots to discover the basics of metaanalysis. I think meta-analysis is so central to how science should be done that every introductory statistics course should include an encounter with it, and forest plots are the pictures that make that easy. Here’s the menu for this chapter:

• Meta-analysis on a small scale • The forest plot for Lucky and Noluck, and the basics of forest plots • What the Publication Manual says • The story of meta-analysis, and meta-analysis making a difference • Further meta-analysis pages in ESCI

Combining Two or Three Studies

Figure 7.1 is a combination of the CI and meta-analysis presentations of the Lucky and Noluck results. It’s simply a combination of Figures 1.1 and 1.2, and it’s our first forest plot. A forest plot is a picture of CIs that present the results from a number of comparable studies, and

another CI at the bottom that presents the result of a meta-analysis combining the evidence over all the studies. Lewis and Clarke (2001) said it’s called a forest plot because it can look like a forest of lines-there may be dozens of studies each contributing a CI. You could also say it helps us see the forest rather than only the trees. Before we start playing with ESCI, try the following questions, which

ask about your intuitions of small-scale meta-analysis:

7.1 Suppose you have two separate estimates of some ES. The two point estimates are similar, and the two CIs each happen to have MOE = 10 units. (Recall that MOE is the length of one arm of a CI.) Suppose we combine the two results by meta-analysis; what’s your guesstimate of MOE for the result?