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…

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.

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem…

How do people make rich inferences from such sparse data? Recent research has explored this inferential ability by investigating probabilistic reasoning in infancy. For example, 8- and 11-month-old infants can make inferences from samples to populations and vice versa (Denison & Xu, 2010a; Xu & Denison, 2009; Xu & Garcia, 2008a). The…

Repeating an item in a list benefits recall performance, and this benefit increases when the repetitions are spaced apart (Madigan, 1969; Melton, 1970). Retrieved context theory incorporates 2 mechanisms that account for these effects: contextual variability and study-phase retrieval. Specifically, if an item presented at position "i" is…

Endress and Mehler (2009) reported that when adult subjects are exposed to an unsegmented artificial language composed from trisyllabic words such as ABX, YBC, and AZC, they are unable to distinguish between these words and what they coined as the "phantom-word" ABC in a subsequent test. This suggests that statistical learning generates knowledge…

Tossing a fair coin 1000 times can have an unexpected result. In the activities presented here, players keep track of the accumulated total for heads and tails after each toss, noting which player is in the lead or whether the players are tied. The winner is the player who was in the lead for the higher number of turns over the course of the game.…

In a previous gaze-contingent boundary experiment, Angele and Rayner (2013) found that readers are likely to skip a word that appears to be the definite article "the" even when syntactic constraints do not allow for articles to occur in that position. In the present study, we investigated whether the word frequency of the preview of a…

As a result of the use of random assignment to treatment, randomized experiments typically have high internal validity. However, units are very rarely randomly selected from a well-defined population of interest into an experiment; this results in low external validity. Under nonrandom sampling, this means that the estimate of the sample average…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

We consider the estimation of probabilistic ranking models in the context of conjoint experiments. By using approximate rather than exact ranking probabilities, we avoided the computation of high-dimensional integrals. We extended the approximation technique proposed by Henery (1981) in the context of the Thurstone-Mosteller-Daniels model to any…

Despite the importance of both response probability and response time for testing models of choice, there is a dearth of chronometric studies examining systematic asymmetries that occur over time- and space-orders in the method of paired comparisons. In this study, systematic asymmetries in discriminating the magnitude of paired visual stimuli are…

In most school achievement research, the relationships between achievement and explanatory variables follow the Newton and Einstein concept/principle and the viewpoint of the macro-observer: Deterministic measures based on the mean value of a sufficiently large number of schools. What if the relationships between achievement and explanatory…

We find the correlation of two jointly distributed random variables connected with a coin tossing experiment. The marginal distributions are binomial and negative binomial.

Concepts in probability can be more readily understood if students are first exposed to probability via experiment. Performing probability experiments encourages students to develop understandings of probability grounded in real events, as opposed to merely computing answers based on formulae.