This primer systematizes the emerging literature on causal inference using deep neural networks under the potential outcomes framework. It provides an intuitive introduction to building and optimizing custom deep learning models and shows how to adapt them to estimate/predict heterogeneous treatment effects. It also discusses ongoing work to…

In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer,…

This note is concerned with the study of temporal development in several indices reflecting clustering effects in multilevel designs that are frequently utilized in educational and behavioral research. A latent variable method-based approach is outlined, which can be used to point and interval estimate the growth or decline in important functions…

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…

The Gini index is probably the most commonly used indicator to measure inequality. For continuous distributions, the Gini index can be computed using several equivalent formulations. However, this is not the case with discrete distributions, where controversy remains regarding the expression to be used to estimate the Gini index. We attempt to…

"Simulation-based inference" is often considered a pedagogical strategy for helping students develop inferential reasoning, for example, giving them a visual and concrete reference for deciding whether the observed statistic is unlikely to happen by chance alone when the null hypothesis is true. In this article, we highlight for teachers…

Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this…

Most existing solutions to the current replication crisis in science address only the factors stemming from specific poor research practices. We introduce a novel mechanism that leverages the experts' predictive abilities to analyze the root causes of replication failures. It is backed by the principle that the most accurate predictor is the most…

Directed acyclic graphs (DAGs) are now a popular tool to inform causal inferences. We discuss how DAGs can also be used to encode theoretical assumptions about nonprobability samples and survey nonresponse and to determine whether population quantities including conditional distributions and regressions can be identified. We describe sources of…

This paper informs users of data collected in international large-scale assessments (ILSA), by presenting argumentsunderlining the importance of considering two design features employed in these studies. We examine a commonmisconception stating that the uncertainty arising from the assessment design is negligible compared with that arisingfrom the…

Small sample sizes contribute to several problems in research and knowledge advancement. This conceptual replication study confirmed and extended the inflation of type II errors and confidence intervals in correlation analyses of small sample sizes common in kinesiology/exercise science. Current population data (N = 18, 230, & 464) on four…

Combining observational and experimental data for causal inference can improve treatment effect estimation. However, many observational data sets cannot be released due to data privacy considerations, so one researcher may not have access to both experimental and observational data. Nonetheless, a small amount of risk of disclosing sensitive…

The issue of model uncertainty has been gaining interest in education and the social sciences community over the years, and the dominant methods for handling model uncertainty are based on Bayesian inference, particularly, Bayesian model averaging. However, Bayesian model averaging assumes that the true data-generating model is within the…

In our data-driven society, it is essential for students to become statistically literate. A core domain within Statistical Literacy is Statistical Inference, the ability to draw inferences from sample data. Acquiring and applying inferences is difficult for students and, therefore, usually not included in the pre-10th-grade curriculum. However,…

The Programme for International Student Assessment (PISA) introduced creative thinking as an innovative domain in 2022. This paper examines the unique methodological issues in international assessments and the implications of measuring creative thinking within PISA's framework, including stratified sampling, rotated form designs, and a distinct…