The clustered observational study (COS) design is the observational study counterpart to the clustered randomized trial. In a COS, a treatment is assigned to intact groups, and all units within the group are exposed to the treatment. However, the treatment is non-randomly assigned. COSs are common in both education and health services research. In…

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

The aim of this research is to assess the attitudes exhibited by pre-service primary mathematics educators towards statistics, while concurrently investigating the influence of gender on these attitudes. The research methodology employed in this study involved the adaptation of the Survey of Attitudes toward Statistics (SATS-36) to pre-service…

Causal mediation analysis is a popular approach for investigating whether the effect of an exposure on an outcome is through a mediator to better understand the underlying causal mechanism. In recent literature, mediation analysis with multiple mediators has been proposed for continuous and dichotomous outcomes. In contrast, methods for mediation…

The ability of the brain to extract patterns from the environment and predict future events, known as statistical learning, has been proposed to interact in a competitive manner with prefrontal lobe-related networks and their characteristic cognitive or executive functions. However, it remains unclear whether these cognitive functions also possess…

Data literacy for students in nonquantitative fields is important as statistics become the grammar of research and how the world's decisions are made. Statistics courses are typically offered by mathematics or statistics departments or by social and natural sciences such as economics, political science, psychology, and biology. Here we discuss how…

Teachers need instructionally useful data to make timely and appropriate decisions to meet their students with intensive needs (Filderman et al., 2019). Teachers have still experienced difficulty in instructional decision making in response to students' CBM data (Gesel et al., 2021). This is because data itself that was used for simply determining…

In this thesis, I use a combination of simulations and empirical data to demonstrate that a small set of structural and functional principles - the basic tenets of predictive coding theory - succinctly accounts for a very wide range of properties in the language processing system. Predictive coding approximates hierarchical Bayesian inference via…

Teaching and learning undergraduate statistics has been a most challenging task for undergraduate psychology majors (Salkind, 2017). A seasoned statistics instructor consulted with a seasoned instructional designer on a method to improve a particularly demanding course using a performance improvement approach to address learning difficulties she…

This paper presents the results of a systematic scoping literature review of higher education mathematics and statistics support (MSS) evaluation focusing on its impact on students. MSS is defined as any additional organised mathematical and/or statistical aid offered to higher education students outside of their regular programme of teaching by…

The evidence-based decision-making movement often assumes that once evidence is available (e.g., via the What Works Clearinghouse), decision-makers will integrate it into their practice. Research-practice partnership studies have shown this is not always true. In this paper, we argue that instead of assuming research will be useful and used, we…

Meta-regression analyses usually focus on estimating and testing differences in average effect sizes between individual levels of each meta-regression covariate in turn. These metrics are useful but have limitations: they consider each covariate individually, rather than in combination, and they characterize only the mean of a potentially…

Here we demonstrate an inexpensive and straightforward electronic circuit that can be used to generate data in the form of counts, with the same statistical properties as those found in gamma-ray counting experiments. The circuit holds an avalanche Zener diode just below its Zener voltage, which allows for thermal electrons to traverse the in the…

For assessments that use different forms in different administrations, equating methods are applied to ensure comparability of scores over time. Ideally, a score scale is well maintained throughout the life of a testing program. In reality, instability of a score scale can result from a variety of causes, some are expected while others may be…

Score differencing is one of the six categories of statistical methods used to detect test fraud (Wollack & Schoenig, 2018) and involves the testing of the null hypothesis that the performance of an examinee is similar over two item sets versus the alternative hypothesis that the performance is better on one of the item sets. We suggest, to…