It states that all studies share the same true effect size. The fixed-effect model assumes that all effect sizes stem from a single, homogeneous population. Although both are based on different assumptions, there is still a strong link between them, as we will soon see. There are two models which try to answer exactly this question, the fixed-effect model and the random-effects model. A meta-analysis model must therefore explain the reasons why and how much observed study results differ, even though there is only one overall effect. As we learned in Chapter 1.1, one of the ultimate goals of meta-analysis is to find one numerical value that characterizes our studies as a whole, even though the observed effect sizes vary from study to study. We want a mathematical formula that explains how we can find the true effect size underlying all of our studies, based on their observed results. The conceptualization of models as a vehicle for explanation is the hallmark of a statistical “culture” to which, as Breiman ( 2001) famously estimated, 98% of all statisticians adhere.īy specifying a statistical model, we try to find an approximate representation of the “reality” behind our data. This explanatory character of models is deeply ingrained in modern statistics, and meta-analysis is no exception. They are an imitation of life, using a mathematical formula to describe processes in the world around us in an idealized way. Models try to explain the mechanisms that generated our observed data, especially when those mechanisms themselves cannot be directly observed. Typically, a statistical model is like a special type of theory. The data are seen as the product of a black box, and our model aims to illuminate what is going on inside that black box. Our model is used to describe the process through which these observed data were generated. In meta-analyses, the data are effect sizes that were observed in the included studies. When defining a statistical model, we start with the information that is already given to us. Every hypothesis test has its corresponding statistical model. There is a model behind \(t\)-tests, ANOVAs, and regression. In one way or the other, models build the basis of virtually all parts of our statistical toolbox. The ubiquity of models in statistics indicates how important this concept is. There are “linear models,” “generalized linear models,” “mixture models,” “gaussian additive models,” “structural equation models,” and so on.
Statistics is full of “models,” and it is likely that you have heard the term in this context before. Knowledge of the concept behind meta-analytic pooling is needed to make an informed decision which of these two models, along with other analytic specifications, is more appropriate in which context.Ĥ.1 The Fixed-Effect and Random-Effects Modelīefore we specify the meta-analytic model, we should first clarify what a statistical model actually is. In statistics, this “idea” translates to a model, and we will have a look at what the meta-analytic model looks like.Īs we will see, the nature of the meta-analysis requires us to make a fundamental decision right away: we have to assume either a fixed-effect model or a random-effects model. Importantly, we will also discuss the “idea” behind meta-analyses. As we previously mentioned, meta-analysis comes with many “researcher degrees of freedom.” There are a myriad of choices concerning the statistical techniques and approaches we can apply, and if one method is better than the other often depends on the context.īefore we begin with our analyses in R, we therefore have to get a basic understanding of the statistical assumptions of meta-analyses, and the maths behind it. Here, we will focus on functions of the package allows us to tweak many details about the way effect sizes are pooled. There are many packages which allow us to pool effect sizes in R. We can assure you that the time you spent working through the previous chapters was well invested. Thorough preparation is a key ingredient of a good meta-analysis, and will be immensely helpful in the steps that are about to follow.
We have already discussed various topics in this book, including the definition of research questions, guidelines for searching, selecting, and extracting study data, as well as how to prepare our effect sizes.
We hope that you were able to resist the temptation of starting directly with this chapter. Fortunately, we have now reached the core part of every meta-analysis: the pooling of effect sizes. A long and winding road already lies behind us.