Researchers across many fields have called for greater attention to heterogeneity of treatment effects--shifting focus from the average effect to variation in effects between different treatments, studies, or subgroups. True heterogeneity is important, but many reports of heterogeneity have proved to be false, non-replicable, or exaggerated. In…

Exploratory research with large numbers of variables and even larger numbers of relationships is likely to result in frequent Type II errors; that is falsely accepting an incorrect null hypotheses. There are three ways of reducing Type II errors: (1) choosing a lower significance level, which then increases the probability of Type I error; (2)…

Contrasts aptitude by treatment interaction (ATI) and hierarchical linear modeling (HLM) methods for making cross-level inferences between individual-level and group-level factors in school effectiveness research. Recommends HLM when intraclass correlations are high. ATI is suitable when intraclass correlations are low, but partitioning the…

To solve problems of causality and measurement in educational research, this paper combines seven variables into a proposed model of educational productivity on achievement tests. The authors first review psychological models of educational production that relate learning to aptitude and environment, and note that these models do not allow for…