In sample designs, it is commonly recognized that using auxiliary information significantly increases an estimator's precision. This manuscript introduces an weighted strategy for computing the finite population mean using auxiliary information in sample surveys. The equations for the mean squared error ("MSE") of the proposed estimator…

We demonstrate the Stirling formula, approximating the factorial, utilising accessible and elementary methods in an engaging manner.

Missing data are common with large scale assessments (LSAs). A typical approach to handling missing data with LSAs is the use of listwise deletion, despite decades of research showing that approach can be a suboptimal strategy resulting in biased estimates. In order to help researchers account for missing data, we provide a tutorial using R and…

We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

Contemporary sciences, including the didactics of science, employ computational simulations as tools in their academic endeavors. The construction and application of these simulations are of interest to didactics as they contribute to shaping new perspectives on scientific activity. Consequently, they warrant special attention in…

The aim of this study was to determine how 5-year-old children identified the functional relationship of correspondence, and whether or not they generalized when working on a task that involved programmable robots. We conducted this study with 15 children (9 girls and 6 boys) in their last year of preschool education. The study was designed around…

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…

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…