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Testing and Interpreting Interaction Effects  

Jeremy F. Dawson

Researchers often want to test whether the association between two or more variables depends on the value of a different variable. To do this, they usually test interactions, often in the form of moderated multiple regression (MMR) or its extensions. If there is an interaction effect, it means the relationship being tested does differ as the other variable (moderator) changes. While methods for determining whether an interaction exists are well established, less consensus exists about how to understand, or probe, these interactions. Many of the common methods (e.g., simple slope testing, regions of significance, use of Gardner et al.’s typology) have some reliance on post hoc significance testing, which is unhelpful much of the time, and also potentially misleading, sometimes resulting in contradictory findings. A recommended procedure for probing interaction effects involves a systematic description of the nature and size of interaction effects, considering the main effects (estimated after centering variables) as well as the size and direction of the interaction effect itself. Interaction effects can also be more usefully plotted by including both a greater range of moderator values and showing confidence bands. Although two-way linear interactions are the most common in the literature, three-way interactions and nonlinear interactions are also often found. Again, methods for testing these interactions are well known, but procedures for understanding these more complex effects have received less attention—in part because of the greater complexity of what such interpretation involves. For three-way linear interactions, the slope difference test has become a standard form of interpretation and linking the findings with theory; however, this is also prone to some of the shortcomings described for post hoc probing of two-way effects. Descriptions of three-way interactions can be improved by using some of the same principles used for two-way interactions, as well as by the appropriate use of the slope difference test. For nonlinear effects, the complexity is greater still, and a different approach is needed to explain these effects more helpfully, focusing on describing the changing shape of the effects across values of the moderator(s). Some of these principles can also be carried forward into more complex models, such as multilevel modeling, structural equation modeling, and models that involve both mediation and moderation.


Meta-Analysis as a Business Research Method  

Alexander D. Stajkovic and Kayla S. Stajkovic

Mounting complexity in the world, coupled with new discoveries and more journal space to publish the findings, have spurred research on a host of topics in just about every discipline of social science. Research forays have also generated unprecedented disagreements. For many topics, empirical findings exist but results are mixed: some show positive relationships, some show negative relationships, and some show no statistically significant relationship. How, then, do researchers go about discovering systematic variation across studies to understand and predict forces that impinge on human functioning? Historically, qualitative literature reviews were performed in conjunction with the counting of statistically significant effects. This approach fails to consider effect magnitudes and sample sizes, and thus its conclusions can be misleading. A more precise way to reach conclusions from research literature is via meta-analysis, defined as a set of statistical procedures that enable researchers to derive quantitative estimates of average and moderator effects across available studies. Since its introduction in 1976, meta-analysis has developed into an authoritative source of information for ascertaining the generalizability of research findings. Thus, it is perhaps not surprising that meta-analyses in the field of management garner, on average, three times as many citations as single studies. A framework for conducting meta-analysis explains why it should be used, outlines what it has yielded to society, and introduces the reader to a fundamental conception and a misconception. More specifics follow about data collection and study selection criteria and implications of publication bias. How to convert estimates from individual studies to a common scale to be able to average them, what to consider in choosing a meta-analytic method, how to compare the procedures, and what information to include when reporting results are presented next. The article concludes with a discussion of nuances and limitations, and suggestions for future research and practice. Science builds knowledge cumulatively from numerous studies, which, more often than not, differ in their characteristics (e.g., research design, participants, setting, sample size). Some findings are in concert and some are not. Through its quantitative foundations, conjoint with theory-guiding hypotheses, meta-analysis offers statistical means of analyzing disparate research designs and conflicting results and discovering consistencies in a seemingly inconsistent literature. Research conclusions reached by a theory-driven, well-conducted meta-analysis are almost certainly more accurate and reliable than those from any single study.