Two novel proofs show that the sum of a specific pair of normal random variables is not normal are established in this note. This is one of the most often misunderstood facts by first-year students in probability theory and statistics. The first proof is concise using the moment generating function. The second proof checks whether the moments of…

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…

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.

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…

The primary objective of this investigation is the formulation of random intercept latent profile transition analysis (RI-LPTA). Our simulation investigation suggests that the election between LPTA and RI-LPTA for examination has negligible impact on the estimation of transition probability parameters when the population parameters are generated…

Over the past ten years, propensity score methods have made an important contribution to improving generalizations from studies that do not select samples randomly from a population of inference. However, these methods require assumptions and recent work has considered the role of bounding approaches that provide a range of treatment impact…

For estimation of heterogeneity variance T[superscript 2] in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized Q statistic, Q[subscript F], in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators…

To explore the differential impact of job automation for different groups of primary and secondary school students, an analysis of variance was conducted using survey data on the occupational aspirations of British school students (aged 7-18) and probability statistics derived from a model of job automation. Results indicated that students aged…

This study explores the usefulness of covariates on equating test scores from nonequivalent test groups. The covariates are captured by an estimated propensity score, which is used as a proxy for latent ability to balance the test groups. The objective is to assess the sensitivity of the equated scores to various misspecifications in the…

Constantly on the lookout for and with a vested interest in Canadian mathematics education matters, because if Canadian mathematics education matters then Canadian mathematics education matters, this article is an investigation into the Canadian lottery landscape. With apologies to the Atlantic Lottery, Loto-Québec and Ontario Lottery and Gaming,…

Propensity score matching and weighting methods are applied to balance covariates and reduce selection bias in the analysis of observational study data, and ultimately estimate a treatment effect. We wish to evaluate the impact of a Supplemental Instruction (SI) program on student success in an Introductory Statistics course. In such student…

The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a robust inference for internal validity, that is, the PIV, as a robustness index…

In this article Danielle Marie Greene-Bell and Francis A. Pearman II examine racial disparities in school closures across the United States, with a particular interest in majority Black schools. Using survival analysis and longitudinal data, they find that majority Black schools are far more likely to close than non-majority Black schools and that…

In this paper we use historic score-reporting records and test-taker metadata to inform data-driven recommendations that support international students in their choice of undergraduate institutions for study in the United States. We investigate the use of Structural Topic Modeling (STM) as a context-aware, probabilistic recommendation method that…

The interactive learning is a continuous process, which is full of a large number of learning interaction activities. The data generated between learners and learning interaction activities can reflect the online learning behaviors. Through the correlation analysis among learning interaction activities, this paper discusses the potential…