Equating error is usually small relative to the magnitude of measurement error, but it could be one of the major sources of error contributing to mean scores of large groups in educational measurement, such as the year-to-year state mean score fluctuations. Though testing programs may routinely calculate the standard error of equating (SEE), the…

The 0.05 boundary within Null Hypothesis Statistical Testing (NHST) "has made a lot of people very angry and been widely regarded as a bad move" (to quote Douglas Adams). Here, we move past meta-scientific arguments and ask an empirical question: What is the psychological standing of the 0.05 boundary for statistical significance? We…

In this study, Kernel test equating methods were compared under NEAT and NEC designs. In NEAT design, Kernel post-stratification and chain equating methods taking into account optimal and large bandwidths were compared. In the NEC design, gender and/or computer/tablet use was considered as a covariate, and Kernel test equating methods were…

Test takers wishing to gain an unfair advantage often share answers with other test takers, either sharing all answers (a full key) or some (a partial key). Detecting key sharing during a tight testing window requires an efficient, easily interpretable, and rich form of analysis that is descriptive and inferential. We introduce a detection method…

The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

There is increasing interest in using factor scores in structural equation models and there have been numerous methodological papers on the topic. Nevertheless, sum scores, which are computed from adding up item responses, continue to be ubiquitous in practice. It is therefore important to compare simulation results involving factor scores to…

Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and provide examples and tentative explanations of a number of statistical…

Considered normative from the second half of the 20th century (Danziger, 1990), null hypothesis statistical testing (NHST) has received consistent, largely unheeded criticism. Critiques have received more attention in recent years with the recognition of the replication crisis in the social sciences and the American Statistical Society's statement…

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent attributes are assumed by researchers to characterize their dependence structure. Specifically, a directed acyclic…

The rise of online proctoring potentially provides more opportunities for item harvesting and consequent brain dumping and shared "study guides" based on stolen content. This has increased the need for rapid approaches for evaluating and acting on suspicious test responses in every delivery modality. Both hiring proxy test takers and…

Previous simulation studies of randomization tests applied in single-case educational intervention research contexts have typically focused on A-to-B phase changes in means/levels. In the present simulation study, we report the results of two multiple-baseline investigations, one targeting between-phase changes in slopes/trends and the other…

Quantitative evidence synthesis methods aim to combine data from multiple medical trials to infer relative effects of different interventions. A challenge arises when trials report continuous outcomes on different measurement scales. To include all evidence in one coherent analysis, we require methods to "map" the outcomes onto a single…

Researchers often have hypotheses concerning the state of affairs in the population from which they sampled their data to compare group means. The classical frequentist approach provides one way of carrying out hypothesis testing using ANOVA to state the null hypothesis that there is no difference in the means and proceed with multiple comparisons…

For ease of instruction in the classroom, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. Likewise, the Kruskal-Wallis statistic may be rewritten in terms of pairwise differences in individual…

Multivariate analysis of variance (MANOVA) is widely used to test the null hypothesis of equal multivariate means across 2 or more groups. MANOVA rests upon an assumption that error terms are independent of one another, which can be violated if individuals are clustered or nested within groups, such as schools. Ignoring such nesting can result in…