Methods for group comparisons using predicted probabilities and marginal effects on probabilities are developed for regression models for binary outcomes. Unlike approaches based on the comparison of regression coefficients across groups, the methods we propose are unaffected by the scalar identification of the coefficients and are expressed in…

The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a robust inference for internal validity, that is, the PIV, as a robustness index…

The purpose of this study was to compare and contrast frameworks for evaluating methodological rigor in single case research. Specifically, research on high-probability requests to increase compliance in young children was evaluated. Ten studies were identified and were coded using 4 frameworks. These frameworks were the Council for Exceptional…

The interactive learning is a continuous process, which is full of a large number of learning interaction activities. The data generated between learners and learning interaction activities can reflect the online learning behaviors. Through the correlation analysis among learning interaction activities, this paper discusses the potential…

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

Online software systems are extensively used to give students practice on course content, especially in mathematics and physics courses. They offer instant feedback, and several of these systems are open source or very economical compared with hiring graders for traditional paper-and-pencil-based homework (PPH). In this article, the authors…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

Since the seminal introduction of the propensity score (PS) by Rosenbaum and Rubin, PS-based methods have been widely used for drawing causal inferences in the behavioral and social sciences. However, the PS approach depends on the ignorability assumption: there are no unobserved confounders once observed covariates are taken into account. For…

What are the cognitive mechanisms underlying subjective valuations formed on the basis of sequential experiences of an option's possible outcomes? Ashby and Rakow (2014) have proposed a sliding window model (SWIM), according to which people's valuations represent the average of a limited sample of recent experiences (the size of which is estimated…

Given the necessity to bridge the gap between what happened and what is likely to happen, this paper aims to explore how to apply Bayesian inference to cost-effectiveness analysis so as to capture the uncertainty of a ratio-type efficiency measure. The first part of the paper summarizes the characteristics of the evaluation data that are commonly…

When performing a meta-analysis unexplained variation above that predicted by within study variation is usually modeled by a random effect. However, in some cases, this is not sufficient to explain all the variation because of outlier or unusual studies. A previously described method is to define an outlier as a study requiring a higher random…

We performed a systematic literature search regarding maternal diabetes before and during pregnancy and the risk of autism spectrum disorders (ASD) in the offspring. Of the 178 potentially relevant articles, 12 articles including three cohort studies and nine case-control studies were included in the meta-analysis. Both the meta-analyses of cohort…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

A long-standing challenge for knowledge tracing is how to update estimates of multiple subskills that underlie a single observable step. We characterize approaches to this problem by how they model knowledge tracing, fit its parameters, predict performance, and update subskill estimates. Previous methods allocated blame or credit among subskills…