Online collaborative discussion (OCD) focuses on promoting individual knowledge inquiry and group knowledge construction through active peer interactions and communications. In practice, it is necessary to explore how different modes of OCD come into play, in which student engagement can function as an evaluating indicator. To identify student…

The nonequivalent groups with anchor test (NEAT) design is widely used in test equating. Under this design, two groups of examinees are administered different test forms with each test form containing a subset of common items. Because test takers from different groups are assigned only one test form, missing score data emerge by design rendering…

A number of memorable tasks have been revealed through collegial exchanges with underlying philosophical, theoretical, and potentially nefarious motivations. Such was the origin of the probability problem, and the various differences of opinion, presented herein. This article recounts how, together, we explored and disputed the probabilities…

The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

To expand the use of cognitive diagnosis models (CDMs) to longitudinal assessments, this study proposes a bias-corrected three-step estimation approach for latent transition CDMs with covariates by integrating a general CDM and a latent transition model. The proposed method can be used to assess changes in attribute mastery status and attribute…

Evidence of processing costs for unexpected words presented in place of a more expected completion remains elusive in the eye-movement literature. The current study investigated whether such prediction error costs depend on the source of constraint violation provided by the prior context. Participants' eye movements were recorded as they read…

The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

Terence Mills introduces us to Keynsian probability and discusses its implications for teaching probability. The author considers it unlikely that Keynes's theory would replace how we teach probability, but argues that it may make us think more deeply about the use of terms such as chance and probability when used in our lessons.

Although humans often multitask, little is known about how the processing of concurrent tasks is managed. The present study investigated whether adjustments in parallel processing during multitasking are local (task-specific) or global (task-unspecific). In three experiments, participants performed one of three tasks: a primary task or, if this…

Across waves of a panel survey, panel members are repeatedly exposed to the same or very similar survey questions, which might lead to learning effects. We used data from 24 waves of online interviews in a probability-based panel survey to investigate the positive and negative effects of becoming more familiar with the survey questions. We found…

This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple…

While foster youth miss more school versus their non-foster counterparts, their status as a foster youth is not static, with many of them entering and exiting the foster care system over time. These dynamics of entry and exit can represent particularly crucial transition periods of stability and instability that may differentially influence…

Thinking probabilistically is an essential part of thinking statistically, and the probability learning objectives that this article focuses on are those that are important in the underpinning of statistics and statistical models. Like mathematical statistics, probability can be considered purely from a mathematical viewpoint, but the focus here…

This paper uses actual data on horse racing to illustrate probabilities, odds, and expected values, and offers cautionary remarks about applying textbook formulas to gambling on real-world sporting events.

We consider the problem of bias arising from conditioning on a post-outcome collider. We illustrate this with reference to Elwert and Winship (2014) but we go beyond their study to investigate the extent to which inverse probability weighting might offer solutions. We use linear models to derive expressions for the bias arising in different kinds…