Most researchers receive formal training in frequentist statistics during their undergraduate studies. In particular, hypothesis testing is usually rooted on the null hypothesis significance testing paradigm and its p-value. Null hypothesis Bayesian testing and its so-called Bayes factor are now becoming increasingly popular. Although the Bayes…

This article develops a set-theoretic approach to Bayes's theorem and Bayesian process tracing. In the approach, hypothesis testing is the procedure whereby one updates beliefs by narrowing the range of states of the world that are regarded as possible, thus diminishing the domain in which the actual world can reside. By explicitly connecting…

This dissertation consists of three manuscripts. The manuscripts contribute to a budding "methodological reform" currently taking place in quantitative second-language (L2) research. In the first manuscript, the researcher describes an empirical investigation on the application of two well-known effect size estimators, eta-squared (eta…

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

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…

This article discusses comparisons of means using exploratory and confirmatory approaches. Three methods are discussed: hypothesis testing, model selection based on information criteria, and Bayesian model selection. Throughout the article, an example is used to illustrate and evaluate the two approaches and the three methods. We demonstrate that…

Null hypothesis testing (NHT) is the most commonly used tool in empirical psychological research even though it has several known limitations. It is argued that since the hypotheses evaluated with NHT do not reflect the research-question or theory of the researchers, conclusions from NHT must be formulated with great modesty, that is, they cannot…

Researchers often have expectations about the research outcomes in regard to inequality constraints between, e.g., group means. Consider the example of researchers who investigated the effects of inducing a negative emotional state in aggressive boys. It was expected that highly aggressive boys would, on average, score higher on aggressive…

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…

This article explores the potential of Bayesian inference as a theoretical framework for describing how people evaluate hypotheses. First, it identifies a set of logically possible forms of non-Bayesian behavior. Second, it reviews existing research in a variety of areas to see whether these possibilities are ever realized. (Author/BW)

This article compares three models that have been the foundation for approaches to the analysis of statistical significance in early childhood research--the Fisherian and the Neyman-Pearson models (both considered "classical" approaches), and the Bayesian model. The article concludes that all three models have a place in the analysis of research…

Thirty-four papers on educational statistics which were presented at the 1971 AERA Conference are summarized. Six major interest areas are covered: (a) general information; (b) non-parametric methods; (c) errors of measurement and correlation techniques; (d) regression theory; (e) univariate and multivariate analysis; (f) factor analysis. (MS)