The existing algorithm employing the log-normal distribution lacks applicability in generating imprecise data. This paper addresses this limitation by first introducing the log-normal distribution as a means to handle imprecise data. Subsequently, we leverage the neutrosophic log-normal distribution to devise an algorithm specifically tailored for…

Background: The generalizability of a study refers to the extent to which the results and inferences from a sample apply to individuals in a larger target population of inference (Shadish et al., 2002). In practice, the strongest tool to facilitate generalizations is random or probability sampling, which is rare in educational studies (Olsen et…

It is an important point to test the homogeneity of variances in statistical methods such as the t-test or F-test used to make comparisons between groups. An erroneous decision regarding the homogeneity of variances will affect the test to be selected and thus lead to different results. For this reason, there are many tests for homogeneity of…

In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer,…

In this paper, we investigate the conditions under which data imbalances, a common data characteristic that occurs when factor values are unevenly distributed, are problematic for the performance of Coincidence Analysis (CNA). We further examine how such imbalances relate to fragmentation and noise in data. We show that even extreme data…

Educational researchers often report effect sizes in standard deviation units (SD), but SD effects are hard to interpret. Effects are easier to interpret in percentile points, but converting SDs to percentile points involves a calculation that is not transparent to educational stakeholders. We show that if the outcome variable is normally…

A single discrete random variable is depicted by a stick diagram, a 2D picture. Naturally, to visualize a bivariate discrete distribution, one can use a bivariate stick diagram, a 3D picture. Unfortunately, many students have difficulty understanding and processing 3D pictures. Therefore, we construct an alternative 2D disc plot to depict the…

This study considers the estimation of marginal reliability and conditional accuracy measures using a generalized recursion procedure with several IRT-based ability and score estimators. The estimators include MLE, TCC, and EAP abilities, and corresponding test scores obtained with different weightings of the item scores. We consider reliability…

Purpose: This paper aims to examine the key domains and prevailing trends in the context of teacher effectiveness while proposing directions for future research in this area. Design/methodology/approach: Utilising the Science Citation Index Expanded and Social Sciences Citation Index databases within Scopus, covering the period from 2014 to 2024,…

Bayesian estimations of complex regression models with high-dimensional parameter spaces require advanced priors, capable of addressing both sparsity and multicollinearity in the data. The Dirichlet-horseshoe, a new prior distribution that combines and expands on the concepts of the regularized horseshoe and the Dirichlet-Laplace priors, is a…

In Savalei's (2011) simulation that evaluated the performance of polychoric correlation estimates in small samples, two methods for treating zero-frequency cells, adding 0.5 (ADD) and doing nothing (NONE), were compared. Savalei tentatively suggested using ADD for binary data and NONE for data with three or more categories. Yet, Savalei's…

Use of artificial intelligence (AI) to score responses is growing in popularity and likely to increase. Evidence of the validity of scores relies on quadratic weighted kappa (QWK) to demonstrate agreement between AI scores and human ratings. QWK is a measure of agreement that accounts for chance agreement and the ordinality of the data by giving…

Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were…

We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates C includes cluster-level partially observed covariates with interaction effects. Due to small sample sizes from 37 patient-physician encounters repeatedly…

The development of new statistical models for the meta-analysis of diagnostic test accuracy studies is still an ongoing field of research, especially with respect to summary receiver operating characteristic (ROC) curves. In the recently published updated version of the "Cochrane Handbook for Systematic Reviews of Diagnostic Test…