In tests with time limits, items at the end are often not reached. Usually, the pattern of missing responses depends on the ability level of the respondents; therefore, missing data are not ignorable in statistical inference. This study models data using a combination of two item response theory (IRT) models: one for the observed response data and…

Processing language requires the retrieval of concepts from memory in response to an ongoing stream of information. This retrieval is facilitated if one can infer the gist of a sentence, conversation, or document and use that gist to predict related concepts and disambiguate words. This article analyzes the abstract computational problem…

People's reactions to coincidences are often cited as an illustration of the irrationality of human reasoning about chance. We argue that coincidences may be better understood in terms of rational statistical inference, based on their functional role in processes of causal discovery and theory revision. We present a formal definition of…

Presents a fully Bayesian analysis for the Probability Matrix Decomposition (PMD) model using the Gibbs sampler. Identifies the advantages of this approach and illustrates the approach by applying the PMD model to opinions of respondents from different countries concerning the possibility of contracting AIDS in a specific situation. (SLD)

This paper comments on the response offered by Trafimow on Lee and Wagenmakers comments on Trafimow's original article. It seems our comment should have made it clear that the objective Bayesian approach we advocate views probabilities neither as relative frequencies nor as belief states, but as degrees of plausibility assigned to propositions in…

The national lottery is often portrayed as a game of pure chance with no room for strategy. This misperception seems to stem from the application of probability instead of expectancy considerations, and can be utilized to introduce the statistical concept of expectation.

Probability is an important idea with a remarkably wide range of applications. However, psychological and instructional studies conducted in the last two decades have consistently documented poor understanding of probability among different populations across different settings. The purpose of this study is to develop a theoretical framework for…

This study examined the internal consistency and validity of a new rating scale to identify gifted students, the Gifted Rating Scales-School Form (GRS-S). The study explored the effect of gender, race/ethnicity, age, and rater familiarity on GRS-S ratings. One hundred twenty-two students in first to eighth grade from elementary and middle schools…

The Behrens-Fisher problem arises when one seeks to make inferences about the means of two normal populations without assuming the variances are equal. This paper presents a review of fundamental concepts and applications used to address the Behrens-Fisher problem under fiducial, Bayesian, and frequentist approaches. Methods of approximations to…

This article describes an illustration of Bayesian inference that has proved popular with students.

This study presents the results of a partial credit Rasch analysis of in-depth interview data exploring statistical understanding of 73 school students in 6 contextual settings. The use of Rasch analysis allowed the exploration of a single underlying variable across contexts, which included probability sampling, representation of temperature…

This paper asserts that causality is an intriguing but controversial topic in philosophy, statistics, and educational and psychological research. By supporting the Causal Markov Condition and the faithfulness condition, Clark Glymour attempted to draw causal inferences from structural equation modeling. According to Glymour, in order to make…

Many evaluation students are still being taught the use of tests of statistical significance without being warned about their limitations. This paper discusses other estimates of treatment effects necessary to interpret between-group differences correctly. Sources to improve evaluation practice are also suggested. (SLD)

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute…

Many research-related classes in social sciences present probability as a unified approach based upon mathematical axioms, but neglect the diversity of various probability theories and their associated philosophical assumptions. Although currently the dominant statistical and probabilistic approach is the Fisherian tradition, the use of Fisherian…