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…

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…

This article presents a step-by-step guide to using R and SPSS to bootstrap exam questions. Bootstrapping, a versatile nonparametric analytical technique, can help to improve the psychometric qualities of exam questions in the process of quality assurance. Bootstrapping is particularly useful in disciplines such as medical education, where student…

This paper reports on a study concerning the social nature of young students' informal inferential reasoning. Employing inferentialism as a background theory, we examine cognitive and sociocultural aspects of reasoning that arose during group discussions as well as trace relations between those aspects. Following a design experiment approach, we…

"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…

This is a practical guide for applying the Impact Threshold for a Confounding Variable and the Robustness of Inference to Replacement using the konfound packages in Stata and R as well as the R-shiny app. It includes motivation worked examples, and tutorials.

Large language models (LLMs) provide cost-effective but possibly inaccurate predictions of human behavior. Despite growing evidence that predicted and observed behavior are often not "interchangeable," there is limited guidance on using LLMs to obtain valid estimates of causal effects and other parameters. We argue that LLM predictions…

Social science theories often postulate systems of causal relationships among variables, which are commonly represented using directed acyclic graphs (DAGs). As non-parametric causal models, DAGs require no assumptions about the functional form of the hypothesized relationships. Nevertheless, to simplify empirical evaluation, researchers typically…

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…

Causal inference is a fundamental goal of many research endeavors, including scholarship in the field of language education and learning. Randomized controlled trials are considered an ideal design to test causal claims, but not all claims can be subjected to experimental treatment due to ethical and practical constraints. In this article, we…