Procedures for examining whether treatment effects on an outcome are mediated and/or moderated have been well developed and are routinely applied. The mediation question focuses on the intervening mechanism that produces the treatment effect. The moderation question focuses on factors that affect the magnitude of the treatment effect. It is important to note that these two processes may be combined in informative ways, such that moderation is mediated or mediation is moderated. Although some prior literature has discussed these possibilities, their exact definitions and analytic procedures have not been completely articulated. The purpose of this article is to define precisely both mediated moderation and moderated mediation and provide analytic strategies for assessing each.

Although interaction effects are frequently found in experimental studies, field researchers report considerable difficulty in finding theorized moderator effects. Previous discussions of this discrepancy have considered responsible factors including differences in measurement error and use of nonlinear scales. In this article we demonstrate that the differential efficiency of experimental and field tests of interactions is also attributable to the differential residual variances of such interactions once the component main effects have been partialed out. We derive an expression for this residual variance in terms of the joint distribution of the component variables and explore how properties of the distribution affect the efficiency of tests of moderator effects. We show that tests of interactions in field studies will often have less than 20% of the efficiency of optimal experimental tests, and we discuss implications for the design of field studies.

Throughout social and cognitive psychology, participants are routinely asked to respond in some way to experimental stimuli that are thought to represent categories of theoretical interest. For instance, in measures of implicit attitudes, participants are primed with pictures of specific African American and White stimulus persons sampled in some way from possible stimuli that might have been used. Yet seldom is the sampling of stimuli taken into account in the analysis of the resulting data, in spite of numerous warnings about the perils of ignoring stimulus variation (Clark, 1973; Kenny, 1985; Wells & Windschitl, 1999). Part of this failure to attend to stimulus variation is due to the demands imposed by traditional analysis of variance procedures for the analysis of data when both participants and stimuli are treated as random factors. In this article, we present a comprehensive solution using mixed models for the analysis of data with crossed random factors (e.g., participants and stimuli). We show the substantial biases inherent in analyses that ignore one or the other of the random factors, and we illustrate the substantial advantages of the mixed models approach with both hypothetical and actual, well-known data sets in social psychology (Bem, 2011; Blair, Chapleau, & Judd, 2005; Correll, Park, Judd, & Wittenbrink, 2002).

Using a simple videogame, the effect of ethnicity on shoot/don't shoot decisions was examined. African American or White targets, holding guns or other objects, appeared in complex backgrounds. Participants were told to "shoot" armed targets and to "not shoot" unarmed targets. In Study 1, White participants made the correct decision to shoot an armed target more quickly if the target was African American than if he was White, but decided to "not shoot" an unarmed target more quickly if he was White. Study 2 used a shorter time window, forcing this effect into error rates. Study 3 replicated Study 1's effects and showed that the magnitude of bias varied with perceptions of the cultural stereotype and with levels of contact, but not with personal racial prejudice. Study 4 revealed equivalent levels of bias among both African American and White participants in a community sample. Implications and potential underlying mechanisms are discussed.

In seems there are two dimensions that underlie most judgments of traits, people, groups, and cultures. Although the definitions vary, the first makes reference to attributes such as competence, agency, and individualism, and the second to warmth, communality, and collectivism. But the relationship between the two dimensions seems unclear. In trait and person judgment, they are often positively related; in group and cultural stereotypes, they are often negatively related. The authors report 4 studies that examine the dynamic relationship between these two dimensions, experimentally manipulating the location of a target of judgment on one and examining the consequences for the other. In general, the authors' data suggest a negative dynamic relationship between the two, moderated by factors the impact of which they explore.