The Karlson-Holm-Breen (KHB) method has rapidly become popular as a way of separating the impact of confounding from rescaling when comparing conditional and unconditional parameter estimates in nonlinear probability models such as the logit and probit. In this note, we show that the same estimates can be obtained in a somewhat different way to…

The standard regression technique for modeling binary response variables in education research is logistic regression. The odds ratios from these models are used to quantify and communicate variable effects. These effects are sometimes pooled together as in a meta-analysis. We argue that this process is problematic as odds ratios calculated from…

Propensity score methods account for selection bias in observational studies. However, the consistency of the propensity score estimators strongly depends on a correct specification of the propensity score model. Logistic regression and, with increasing popularity, machine learning tools are used to estimate propensity scores. We introduce a…

This article asks the question: is the "Last Banana" game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by…

In late November 2020, there was a flurry of media coverage of two companies' claims of 95% efficacy rates of newly developed COVID-19 vaccines, but information about the confidence interval was not reported. This paper presents a way of teaching the concept of hypothesis testing and the construction of confidence intervals using numbers announced…

Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it…

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…

This report aims to showcase the value of implementing a Bayesian framework to analyse and report results from international large-scale surveys and provide guidance to users who want to analyse the data using this approach. The motivation for this report stems from the recognition that Bayesian statistical inference is fast becoming a popular…

The effect sizes of studies included in a meta-analysis do often not share a common true effect size due to differences in for instance the design of the studies. Estimates of this so-called between-study variance are usually imprecise. Hence, reporting a confidence interval together with a point estimate of the amount of between-study variance…

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…

Unusual response similarity among test takers may occur in testing data and be an indicator of potential test fraud (e.g., examinees copy responses from other examinees, send text messages or pre-arranged signals among themselves for the correct response, item pre-knowledge). One index to measure the degree of similarity between two response…

Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

This review covers the core concepts and design decisions of TensorFlow. TensorFlow, originally created by researchers at Google, is the most popular one among the plethora of deep learning libraries. In the field of deep learning, neural networks have achieved tremendous success and gained wide popularity in various areas. This family of models…

Employing nested sequences of models is a common practice when exploring the extent to which one set of variables mediates the impact of another set. Such an analysis in the context of logistic regression models confronts two challenges: (1) direct comparisons of coefficients across models are generally biased due to the changes in scale that…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…