The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact,…

Access to high-quality education at scale is limited by the difficulty of providing student feedback on open-ended assignments in structured domains like programming, graphics, and short response questions. This problem has proven to be exceptionally difficult: for humans, it requires large amounts of manual work, and for computers, until…

The analysis of covariance (ANCOVA) is a useful statistical procedure that incorporates covariate features into the adjustment of treatment effects. The consequences of omitted prognostic covariates on the statistical inferences of ANCOVA are well documented in the literature. However, the corresponding influence on sample-size calculations for…

Administrative problems such as computer malfunction and power outage occasionally lead to missing item scores and hence to incomplete data on mastery tests such as the AP and U.S. Medical Licensing examinations. Investigators are often interested in estimating the probabilities of passing of the examinees with incomplete data on mastery tests.…

Although much research has been conducted on the psychometric properties of cognitive diagnostic models, they are only recently being used in operational settings to provide results to examinees and other stakeholders. Using this newer class of models in practice comes with a fresh challenge for diagnostic assessment developers: effectively…

In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons…

Although the root-mean squared deviation (RMSD) is a popular statistical measure for evaluating country-specific item-level misfit (i.e., differential item functioning [DIF]) in international large-scale assessment, this paper shows that its sensitivity to detect misfit may depend strongly on the proficiency distribution of the considered…

BKT and other classical student models are designed for binary environments where actions are either correct or incorrect. These models face limitations in open-ended and data-driven environments where actions may be correct but non-ideal or where there may even be degrees of error. In this paper we present BKT-SR and RKT-SR: extensions of the…

Assessment is fundamental to school psychology, but its purpose has shifted from making predictions about children to improving outcomes for children. This commentary on the special issue focuses on screening and progress-monitoring decisions that can be used to solve student problems. We outline several psychometric and practical issues that…

Fine-grained data on religious communities are often considered sensitive in South Asia and consequently remain inaccessible. Yet without such data, statistical research on communal relations and group-based inequality remains superficial, hampering the development of appropriate policy measures to prevent further social exclusion on the basis of…

As an assessment method based on a constructivist approach, peer assessment has become popular in recent years. However, in peer assessment, a problem remains that reliability depends on the rater characteristics. For this reason, some item response models that incorporate rater parameters have been proposed. Those models are expected to improve…

This manuscript discusses the common confusion between the terms probability and odds. To emphasize the importance and responsibility of being meticulous in the dissemination of information and knowledge, this manuscript reveals five cases of sources of inaccurate statistical language imbedded in the dissemination of information to the general…

This paper describes and evaluates the use of measurement decision theory (MDT) to classify examinees based on their item response patterns. The model has a simple framework that starts with the conditional probabilities of examinees in each category or mastery state responding correctly to each item. The presented evaluation investigates: (1) the…

This article describes a model that can be used to analyze student enrollment data and can give insights for improving retention of part-time students and refining institutional budgeting and planning efforts. Adult higher-education programs are often challenged in that part-time students take courses less reliably than full-time students. For…