This paper proposes an extension of linear equating that may be useful in one of two fairly common assessment scenarios. One is where different students have taken different combinations of test forms. This might occur, for example, where students have some free choice over the exam papers they take within a particular qualification. In this…

Grouping students according to their abilities and promoting deeper interaction and moderation are key issues in improving computational thinking in collaborative programming. However, the distribution characteristics and evolving pathways of computational thinking in different groups have not been deeply explored. During the course of a…

Educational researchers often report effect sizes in standard deviation units (SD), but SD effects are hard to interpret. Effects are easier to interpret in percentile points, but converting SDs to percentile points involves a calculation that is not transparent to educational stakeholders. We show that if the outcome variable is normally…

Background/Context: Single-case experiment designs (SCEDs) are experimental designs in which a small number of cases are repeatedly measured over time, with manipulation of baseline and intervention phases. Because SCEDs often rely on direct behavioral observations, count data are common. To account for both the clustering and the non-normal…

Background: Double/debiased machine learning (DML) methods have been proposed to overcome the regularization bias from the naive approach of ML methods (Chernozhukov et al., 2018). DML methods use a partialling-out approach which removes the effect of confounders from both the treatment and outcome and then regresses the residualized outcome on…

Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected…

Computational learning theory studies the design and analysis of learning algorithms, and it is integral to the foundation of machine learning. In the modern era, classical computational learning theory is growingly unable to catch up with new practical demands. In particular, problems arise in the following aspects: i). "scalability":…

This study compared the weekly training load (TL) variation across different measures. Fifty-two runners reported their heart rate and distance ran for each training session during four weeks of training. Heart rate measures were used to calculate the weekly TRaining IMPulse (W-TRIMP), whereas the distance ran was used to calculate the weekly…

Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into…

We explored the practicality of relatively small item pools in the context of low-stakes Computer-Adaptive Testing (CAT), such as CAT procedures that might be used for quick diagnostic or screening exams. We used a basic CAT algorithm without content balancing and exposure control restrictions to reflect low stakes testing scenarios. We examined…

We consider the cascading effects of researcher decisions throughout the process of quantifying racially polarized voting (RPV). We contrast three methods of estimating precinct racial composition, Bayesian Improved Surname Geocoding (BISG), fully Bayesian BISG, and Citizen Voting Age Population (CVAP), and two algorithms for performing ecological…

This study aims to suggest a generalized class of estimators for population proportion under simple random sampling, which uses auxiliary attributes. The bias and MSEs are considered derived to the first degree approximation. The validity of the suggested and existing estimators is assessed via an empirical investigation. The performance of…

In an educational setting, an estimate of the difficulty of Multiple-Choice Questions (MCQs), a commonly used strategy to assess learning progress, constitutes very useful information for both teachers and students. Since human assessment is costly from multiple points of view, automatic approaches to MCQ item difficulty estimation are…

This study investigates the estimation of classification consistency and accuracy indices for composite summed and theta scores within the SS-MIRT framework, using five popular approaches, including the Lee, Rudner, Guo, Bayesian EAP, and Bayesian MCMC approaches. The procedures are illustrated through analysis of two real datasets and further…

Background: One of the most vexing threats to education field trials is attrition--when some subjects drop out before it is complete. Since outcomes are not available for subjects who attrit, they are typically dropped from any analysis estimating average effects on the outcome. However, since attrition may itself have been affected by treatment…