The product Bayes factor (PBF) synthesizes evidence for an informative hypothesis across heterogeneous replication studies. It can be used when fixed- or random effects meta-analysis fall short. For example, when effect sizes are incomparable and cannot be pooled, or when studies diverge significantly in the populations, study designs, and…

In standardized educational testing, test items are reused in multiple test administrations. To ensure the validity of test scores, the psychometric properties of items should remain unchanged over time. In this article, we consider the sequential monitoring of test items, in particular, the detection of abrupt changes to their psychometric…

This article develops a set-theoretic approach to Bayes's theorem and Bayesian process tracing. In the approach, hypothesis testing is the procedure whereby one updates beliefs by narrowing the range of states of the world that are regarded as possible, thus diminishing the domain in which the actual world can reside. By explicitly connecting…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

Peer-grading is commonly adopted by instructors as an effective assessment method for MOOCs (Massive Open Online Courses) and SPOCs (Small Private online course). For solving the problems brought by varied skill levels and attitudes of online students, statistical models have been proposed to improve the fairness and accuracy of peer-grading.…

In this response, we first show that Simpson's proposed analysis answers a different and less interesting question than ours. We then justify the choice of prior for our Bayes factors calculations, but we also demonstrate that the substantive conclusions of our article are not substantially affected by varying this choice.

The number of articles showing dissatisfaction with the null hypothesis statistical testing (NHST) framework has been progressively increasing over the years. Alternatives to NHST have been proposed and the Bayesian approach seems to have achieved the highest amount of visibility. In this last part of the special issue, a few alternative…

Artificial intelligence-enabled adaptive learning systems (AI-ALS) are increasingly being deployed in education to enhance the learning needs of students. However, educational stakeholders are required by policy-makers to conduct an independent evaluation of the AI-ALS using a small sample size in a pilot study, before that AI-ALS can be approved…

Currently available (classical) testing procedures for the network autocorrelation can only be used for falsifying a precise null hypothesis of no network effect. Classical methods can be neither used for quantifying evidence for the null nor for testing multiple hypotheses simultaneously. This article presents flexible Bayes factor testing…

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

An adaptive learning system is proposed that incorporates a Bayesian network to efficiently gauge learners' understanding at the course-unit level. Also, learners receive content that is adapted to their measured level of understanding. The system works on an iPad via the Edmodo platform. A field experiment using the system in an elementary school…

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…

The purpose of this paper is to provide an easy template for the inclusion of the Bayes factor in reporting experimental results, particularly as a recommendation for articles in the "Journal of Problem Solving." The Bayes factor provides information with a similar purpose to the "p"-value--to allow the researcher to make…

Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue…

Effective assessment is vital in educational activities. We propose IWAS (intelligent Web-based assessment system), an intelligent, generalized and real-time system to assess both learning and teaching. IWAS provides a foundation for more efficiency in instructional activities and, ultimately, students' performances. Our contributions are…