The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Dropping out of university is regularly discussed as a negative indicator. However, research on actual career trajectories of dropouts is virtually non-existent. This study estimates the association between tertiary dropouts and career chances in 15 European countries. Using data from the 2011 Programme for the International Assessment of Adult…

Researchers addressing posttreatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for the subsequent estimation of causal effects in this framework is to use methods based on the "principal score," the conditional probability of belonging…

The article serves as a guide for researchers in developing evidence of validity using bivariate correlations, specifically construct validity. The authors outline the steps for calculating and interpreting bivariate correlations. Additionally, they provide an illustrative example and discuss the implications.

The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

We address the challenging task of "computational natural language inference," by which we mean bridging two or more natural language texts while also providing an explanation of how they are connected. In the context of question answering (i.e., finding short answers to natural language questions), this inference connects the question…

Wollack, Cohen, and Eckerly (2015) suggested the "erasure detection index" (EDI) to detect fraudulent erasures for individual examinees. Wollack and Eckerly (2017) extended the EDI to detect fraudulent erasures at the group level. The EDI at the group level was found to be slightly conservative. This paper suggests two modifications of…

Patient safety is a priority in healthcare today. Good clinician numeracy in doctors contributes to patient safety, since it is essential for accuracy in prescribing, and in data interpretation. Evidence, however, suggests that although doctors are assumed to be highly numerate, they often make errors in drug dose calculation and struggle to…

Obtaining predictions from regression models fit to multiply imputed data can be challenging because treatments of multiple imputation seldom give clear guidance on how predictions can be calculated, and because available software often does not have built-in routines for performing the necessary calculations. This research note reviews how…

This Research Note shows that classic composers created their best works when they were at a similar age when creators in other domains did their best work, namely when they were at an age that represented around 60% of their life span. This finding is very similar to earlier results for painters and authors.

This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…