Background: Clustered randomized controlled trials are commonly used to evaluate the effectiveness of treatments. Frequently, stratified or paired designs are adopted in practice. Fogarty (2018) studied variance estimators for stratified and not clustered experiments and Schochet et. al. (2022) studied that for stratified, clustered RCTs with…

The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord's foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions…

Chaotic phenomena are not part of standard curricula, although this subject offers several interesting aspects which can help students better understand basic features of science. A central observation is that even simple physical systems, if chaotic, are unpredictable, just like the weather. We present the principles applied when developing a…

Clear and rigorous quantum reasoning is needed to explain quantum physical phenomena. As pillars of true quantum physical explanations, we suggest specific quantum reasoning derived from quantum physical key ideas. An experiment is suggested to support such a quantum reasoning, in which a quantized radiation field interacts with an optical beam…

Past research indicates that individuals respond adaptively to contextual factors in multiattribute choice tasks. Yet it remains unclear how this adaptation is cognitively governed. In this article, empirically testable implementations of two prominent competing theoretical frameworks are developed and compared across two multiattribute choice…

Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle's trajectory. Quantum physics is an inherently probabilistic theory in that only…

Having the ability to make informed decisions about health, financial investments, and even the weather are all important to our everyday lives. However, most people receive no formal education on how to read and understand data presented in formats such as data tables and graphs. Research within the field of statistical reasoning demonstrates a…

Identifying patterns in the world requires noticing not only unusual occurrences, but also unusual absences. We examined how people learn from absences, manipulating the extent to which an absence is expected. People can make two types of inferences from the absence of an event: either the event is possible but has not yet occurred, or the event…

Categorical perception (CP) effects manifest as faster or more accurate discrimination between objects that come from different categories compared with objects that come from the same category, controlling for the physical differences between the objects. The most popular explanations of CP effects have relied on perceptual warping causing…

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students' abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis…

A number of probabilistic experiments are described to estimate e, p and v2, with results from computer simulations being used to investigate convergence. A number of possible classroom exercises and extensions are presented.

There is a wealth of evidence that people's reasoning is influenced by explanatory considerations. Little is known, however, about the exact form this influence takes, for instance about whether the influence is unsystematic or because of people's following some rule. Three experiments investigate the descriptive adequacy of a precise proposal to…

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists--such as Einstein--do? Four experiments support the latter possibility. In particular, we…

The authors describe how the Monty Hall Dilemma, a well-known choice anomaly, can be demonstrated with a simple and versatile classroom experiment. In addition to demonstrating the anomaly, the experiment can be used to introduce students to some institutional modifications that have been shown to ameliorate it. This experiment, which can be…

Stimuli that capture the central tendency of presented exemplars are often preferred--a phenomenon also known as the classic beauty-in-averageness effect. However, recent studies have shown that this effect can reverse under certain conditions. We propose that a key variable for such ugliness-in-averageness effects is the category structure of the…