This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

Many existing methods of statistical inference and analysis rely heavily on the assumption that the data are normally distributed. However, the normality assumption is not fulfilled when dealing with data which does not contain negative values or are otherwise skewed--a common occurrence in diverse disciplines such as finance, economics, political…

Randomized controlled trials (RCTs) and quasi-experimental designs like regression discontinuity (RD) designs, instrumental variable (IV) designs, and matching and propensity score (PS) designs are frequently used for inferring causal effects. It is well known that the features of these designs facilitate the identification of a causal estimand…

There is much research that documents what many teachers know, that students struggle with many concepts in probability and statistics. This article presents two sample activities the authors use to help preservice teachers develop ideas about how they can use technology to promote their students' ability to understand mathematics and connect…