Researchers often seek to synthesize results of multiple studies on the same topic to draw statistical or substantive conclusions and to estimate effect sizes that will inform power analyses for future research. The most popular synthesis approach is meta-analysis. There have been few discussions and applications of other synthesis approaches.…

Purpose: This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method: First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors.…

Research questions regarding how, for whom, and where a treatment achieves its effect on an outcome have become increasingly valued in substantive research. Such questions can be answered by causal moderated mediation analysis, which assesses the heterogeneity of the mediation mechanism underlying the treatment effect across individual and…

Multilevel modeling (MLM) is a statistical technique for analyzing clustered data. Despite its long history, the technique and accompanying computer programs are rapidly evolving. Given the complexity of multilevel models, it is crucial for researchers to provide complete and transparent descriptions of the data, statistical analyses, and results.…

The ability of a scientific discipline to build cumulative knowledge depends on its predominant method of data analysis. A steady accumulation of knowledge requires approaches which allow researchers to consider results from comparable prior research. Bayesian statistics is especially relevant for establishing a cumulative scientific discipline,…

The purpose of this paper is to provide an easy template for the inclusion of the Bayes factor in reporting experimental results, particularly as a recommendation for articles in the "Journal of Problem Solving." The Bayes factor provides information with a similar purpose to the "p"-value--to allow the researcher to make…

The authors thank Dr. Lindsay Page for providing a nice illustration of the use of the principal stratification framework to define causal effects, and a Bayesian model for effect estimation. They hope that her well-written article will help expose education researchers to these concepts and methods, and move the field of mediation analysis in…

In his article, "An Alternative to Null-Hypothesis Significance Tests," Killeen (2005) urged the discipline to abandon the practice of "p[subscript obs]"-based null hypothesis testing and to quantify the signal-to-noise characteristics of experimental outcomes with replication probabilities. He described the coefficient that he…

Lecoutre, Lecoutre, and Poitevineau (2010) have provided sophisticated grounding for "p[subscript rep]." Computing it precisely appears, fortunately, no more difficult than doing so approximately. Their analysis will help move predictive inference into the mainstream. Iverson, Wagenmakers, and Lee (2010) have also validated…

P. R. Killeen's (2005a) probability of replication ("p[subscript rep]") of an experimental result is the fiducial Bayesian predictive probability of finding a same-sign effect in a replication of an experiment. "p[subscript rep]" is now routinely reported in "Psychological Science" and has also begun to appear in…

This comment offers three descriptions of "p[subscript rep]" that start with a frequentist account of confidence intervals, draw on R. A. Fisher's fiducial argument, and do not make Bayesian assumptions. Links are described among "p[subscript rep]," "p" values, and the probability a confidence interval will capture…

Demonstrates the consequences on total misdiagnosis rates of using conventional (fixed) rather than flexible (Bayesian) rules when using the Minnesota Multiphasic Personality Inventory in diagnosis. Concludes that the range of base rates and the separation of distributions of normal and abnormal scores affect the difference in the misdiagnosis…

In clinical trials, adaptive allocation means that the therapies assigned to the next patient or patients depend on the results obtained thus far in the trial. Although many adaptive allocation procedures have been proposed for clinical trials, few have actually used adaptive assignment, largely because classical frequentist measures of inference…

Simple Bayesian approaches can be applied to answer specific questions in evaluating an individualized reading program. A small reading and study skills program located in the counseling center of a major research university collected and compiled data on student characteristics such as class, number of sessions attended, grade point average, and…