A Monte Carlo study compared 14 methods to test the statistical significance of the intervening variable effect. An intervening variable (mediator) transmits the effect of an independent variable to a dependent variable. The commonly used R. M. Baron and D. A. Kenny (1986) approach has low statistical power. Two methods based on the distribution of the product and 2 difference-incoefficients methods have the most accurate Type I error rates and greatest statistical power except in 1 important case in which Type I error rates are too high. The best balance of Type I error and statistical power across all cases is the test of the joint significance of the two effects comprising the intervening variable effect.The purpose of this article is to compare statistical methods used to test a model in which an independent variable (X) causes an intervening variable (I), which in turn causes the dependent variable (Y). Many different disciplines use such models, with the terminology, assumptions, and statistical tests only partially overlapping among them. In psychology, the X → I → Y relation is often termed mediation (Baron & Kenny, 1986), sociology originally popularized the term indirect effect (Alwin & Hauser, 1975), and in epidemiology, it is termed the surrogate or intermediate endpoint effect (Freedman & Schatzkin, 1992). This article focuses on the statistical performance of each of the available tests of the effect of an intervening variable. Consideration of conceptual issues related to the definition of intervening variable effects is deferred to the final section of the Discussion.Hypotheses articulating measurable processes that intervene between the independent and dependent variables have long been proposed in psychology (e.g., MacCorquodale & Meehl, 1948;Woodworth, 1928). Such hypotheses are fundamental to theory in many areas of basic and applied psychology (Baron & Kenny, 1986;James & Brett, 1984). Reflecting this importance, a search of the Social Science Citation Index turned up more than 2,000 citations of the Baron and Kenny article that presented an important statistical approach to the investigation of these processes. Examples of hypotheses and models that involve intervening variables abound. In basic social psychology, intentions are thought to mediate the relation between attitude and behavior (Ajzen & Fish-bein, 1980). In cognitive psychology, attentional processes are thought to intervene between stimulus and behavior (Stacy, Leigh, & Weingardt, 1994). In industrial psychology, work environment leads to changes in the intervening variable of job perception, which in turn affects behavioral outcomes (James & Brett, 1984 NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript work on preventive health interventions, programs are designed to change proximal variables, which in turn are expected to have beneficial effects on the distal health outcomes of interest (Hansen, 1992; MacKinnon, 1994;West & Aiken, 1997).A search of psychological abstracts from 1996 to 1999 yi...

The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

Mediating variables are prominent in psychological theory and research. A mediating variable transmits the effect of an independent variable on a dependent variable. Differences between mediating variables and confounders, moderators, and covariates are outlined. Statistical methods to assess mediation and modern comprehensive approaches are described. Future directions for mediation analysis are discussed.

Mediation models are widely used, and there are many tests of the mediated effect. One of the most common questions that researchers have when planning mediation studies is, "How many subjects do I need to achieve adequate power when testing for mediation?" This article presents the necessary sample sizes for six of the most common and the most recommended tests of mediation for various combinations of parameters, to provide a guide for researchers when designing studies or applying for grants.Since the publication of Baron and Kenny's (1986) article describing a method to evaluate mediation, the use of mediation models in the social sciences has increased dramatically. Using the Social Science Citation Index, MacKinnon, Lockwood, Hoffman, West, and Sheets (2002) found more than 2,000 citations of Baron and Kenny's article. A more recent search of the Social Science Citation Index that we conducted found almost 8,000 citations, though a number of these publications examined moderation rather than mediation.Although there are a number of methods to test for mediation, including structural equation modeling (SEM; Cole & Maxwell, 2003;Holmbeck, 1997;Kenny, Kashy, & Bolger, 1998) and bootstrapping (MacKinnon, Lockwood, & Williams, 2004;Shrout & Bolger, 2002), many researchers prefer to use regression-based tests. MacKinnon et al. (2002) investigated power empirically for common sample sizes for many of these tests. However, for researchers planning studies, it would be more useful to know the sample size required for .8 power to detect an effect. The purpose of this article is to offer guidelines for researchers in determining the sample size necessary to conduct mediational studies with .8 statistical power. MEDIATIONIn a mediation model, the effect of an independent variable (X) on a dependent variable (Y) is transmitted through a third intervening, or mediating, variable (M). That is, X causes M, and M causes Y. Figure 1 shows the path diagrams for a simple mediation model; the top diagram represents the total effect of X on Y, and the bottom diagram represents the indirect effect of X on Y through M and the direct effect of X on Y controlling for M. If M is held constant in a model in which the mediator explains all of the variation between X and Y (i.e., a model in which there is complete mediation), then the relationship between X and Y is zero.The path diagrams in Figure 1 can be expressed in the form of three regression equations: where τ̂ is the estimate of the total effect of X on Y, τ′ is the estimate of the direct effect of X on Y adjusted for M, β̂ is the estimate of the effect of M on Y adjusted for X, and α̂ is the estimate of the effect of X on M. ζ̂1, ζ̂2, and ζ̂3 are the intercepts. The product αβ̂ is known as the mediated or indirect effect. MacKinnon et al. (2002) placed the different regression tests of mediation into three categories: tests of causal steps, tests of the difference in coefficients, and tests of the product of coefficients. In the causal-steps approach, each of the four s...

The purpose of this article is to describe statistical procedures to assess how prevention and intervention programs achieve their effects. The analyses require the measurement of intervening or mediating variables hypothesized to represent the causal mechanism by which the prevention program achieves its effects. Methods to estimate mediation are illustrated in the evaluation of a health promotion program designed to reduce dietary cholesterol and a school-based drug prevention program. The methods are relatively easy to apply and the information gained from such analyses should add to our understanding of prevention.