Knowledge tracing (KT) for evaluating students' knowledge is an essential task in personalized education. More and more researchers have devoted themselves to solving KT tasks, e.g., deep knowledge tracing (DKT), which can capture more sophisticated representations of student knowledge. Nonetheless, these techniques ignore the reconstruction of…

In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of post-treatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due…

Beginning with debates about the effects of smoking on lung cancer, sensitivity analyses characterizing the hypothetical unobserved conditions that can alter statistical inferences have had profound impacts on public policy. One of the most ascendant techniques for sensitivity analysis is Oster's (2019) coefficient of proportionality, which…

Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

Missing data in scientific research go hand in hand with assumptions about the nature of the missingness. When dealing with missing values, a set of beliefs has to be formulated about the extent to which the observed data may also hold for the missing parts of the data. It is vital that the validity of these missingness assumptions is verified,…

Bayesian methods seem a natural choice for combining sources of evidence in meta-analyses. However, in practice, their sensitivity to the choice of prior distribution is much less attractive, particularly for parameters describing heterogeneity. A recent non-Bayesian approach to fixed-effects meta-analysis provides novel ways to think about…

Pseudocontingencies are inferences of correlations between variables, like two options and two outcomes, drawn on the basis of their skewed base rates covarying across a third variable (e.g., two contexts). Here, we investigated the effect of pseudocontingency inference on choice behavior. When choices between two options are not based on the…

Recent critiques of physics education research (PER) studies have revoiced the critical issues when drawing causal inferences from observational data where no intervention is present. In response to a call for a "causal reasoning primer" in PER, this paper discusses some of the fundamental issues in statistical causal inference. In…

When fitting unidimensional item response theory (IRT) models, the population distribution of the latent trait ([theta]) is often assumed to be normally distributed. However, some psychological theories would suggest a nonnormal [theta]. For example, some clinical traits (e.g., alcoholism, depression) are believed to follow a positively skewed…

Media articles often communicate the latest scientific findings, and readers must evaluate the evidence and consider its potential implications. Prior work has found that the inclusion of graphs makes messages about scientific data more persuasive (Tal & Wansink, 2016). One explanation for this finding is that such visualizations evoke the…

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 discussion on the role of American Sign Language (ASL) in deaf students' reading development has been long and contentious. The students' limited knowledge of English has been commonly perceived as a culprit in making reading difficult. However, a more nuanced explanation of reading performance and its relationship with competence in ASL's…

Background: The existence of a multiplier, compositional or social context effect is debated extensively in the literature on school effectiveness and also relates to the wider issue of equity in educational outcomes. However, comparatively little attention has been given to whether or not the association between student achievement and school…

This paper analyzes the relationship between proportional reasoning and understanding fair games in Costa Rican students. We conducted a quantitative and qualitative analysis of the answers to six items on comparing ratios of increasing difficulty level and another item on prize estimation in a fair game. We describe the strategies employed and…

Most current statistics courses include some instruction relevant to causal inference. Whether this instruction is incorporated as material on randomized experiments or as an interpretation of associations measured by correlation or regression coefficients, the way in which this material is presented may have important implications for…