The recent commentary by Beaujean and Farmer (2020) on the original paper by Dixon et al. (2019) serves a cautionary tale of selective p-values, the law of small N sizes, and the type-II error. We believe these authors have crafted a somewhat questionable argument in which only 57% of the original Dixon et al. data were re-analyzed, based on a…

The author begins this discussion by thanking Larry Hedges, the editor of the journal, for giving him an opportunity to provide a commentary on this stimulating article. He also would like to congratulate the authors of the article for their insightful discussion on causal mediation analysis, which is one of the most important and challenging…

I discuss the recommendations and cautions in Steinley and Brusco's (2011) article on the use of finite models to cluster a data set. In their article, much use is made of comparison with the "K"-means procedure. As noted by researchers for over 30 years, the "K"-means procedure can be viewed as a special case of finite mixture modeling in which…

On the basis of the statistical concept of waiting time and on computer simulations of the "probabilities of nonoccurrence" (p. 457) for random sequences, Hahn and Warren (2009) proposed that given people's experience of a finite data stream from the environment, the gambler's fallacy is not as gross an error as it might seem. We deal with two…

This article contrasts 2 approaches to analyzing transitivity of preference and other behavioral properties in choice data. The approach of Regenwetter, Dana, and Davis-Stober (2011) assumes that on each choice, a decision maker samples randomly from a mixture of preference orders to determine whether "A" is preferred to "B." In contrast, Birnbaum…

In a recent study, G. Kuhn and Z. Dienes (2005) reported that participants previously exposed to a set of musical tunes generated by a biconditional grammar subsequently preferred new tunes that respected the grammar over new ungrammatical tunes. Because the study and test tunes did not share any chunks of adjacent intervals, this result may be…

The author previously published a paper discussing how to conduct an analysis based on a cluster sample. In that paper, the author outlined several widely adopted alternative approaches, and pointed out that such approaches are anyway not needed for population figures, and not possible for non-probability samples. Thus, the author queried the…

In this article, the author responds to the paper "Exploring pre-service teachers' understanding of statistical variation: Implications for teaching and research" by Sashi Sharma (see EJ779107). In that paper, Sharma described a study "designed to investigate pre-service teachers' acknowledgment of variation in sampling and…

Generally educational research is grounded in the empirical traditions of the social sciences (commonly called quantitative and qualitative methods) and is as such distinguished from other forms of scholarship such as theoretical, conceptual or methodological essays, critiques of research traditions and practices and those studies grounded in the…

In their comment on the tolerance-noise covariation (TNC) method for decomposing variability by H. Muller and D. Sternad (2003, 2004b), J. B. J. Smeets and S. Louw show that covariation (C), as defined within the TNC method, is not invariant with respect to coordinate transformations and contend that it is, therefore, meaningless. Although the…

It has been proposed that it is possible to decompose changes in variability of human motor behavior into 3 independent components: covariation, task tolerance, and stochastic noise. The authors simulate learning to throw accurately and show that for this task the proposed analysis does not give an unambiguous answer to the question of what the 3…

Bell-curve thinking, as a model of distribution of success and failure in society, enjoys a perennial (ahistorical, objective, and law-like) status in education. As such it provides a rationale for sorting (tracking or streaming) practices in education, which has led many educators to criticize both bell-curve thinking and associated sorting…

Probability is an essential tool for understanding heredity and modern genetics, yet many students have difficulty with this topic due to the abstract and quantitative nature of the subject. To facilitate student learning of probability in genetics, we have developed a set of hands-on, cooperative activities that allow students to determine…

Most traditional models, frameworks, and findings that apply to the majority of students and faculty do not adequately apply to important subpopulations. The recommendations here will help researchers become more sensitive to the nuances among various educational subgroups, and to pay more attention to outliers.

Examines and rejects common criticisms of the causality concept; shows causality is a relation implied in the grammar of a language about objects. Discusses objective criteria for concepts of causal relations and explains how the concept of causality may be modified to have causes determine probabilities of outcomes. (Author/RH)