Score differencing is one of 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…

Clustering methods are often used in physics education research (PER) to identify subgroups of individuals within a population who share similar response patterns or characteristics. Among these, k-means (or k-modes, for categorical data) is one of the most commonly used clustering methods in PER. This algorithm, however, is distance-based rather…

For estimation of heterogeneity variance T[superscript 2] in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized Q statistic, Q[subscript F], in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

Standard meta-analysis methods are vulnerable to bias from incomplete reporting of results (both publication and outcome reporting bias) and poor study quality. Several alternative methods have been proposed as being less vulnerable to such biases. To evaluate these claims independently we simulated study results under a broad range of conditions…

Pedagogical content knowledge (PCK) traditionally has been used in research concerning prospective and practicing classroom teachers. This essay argues that PCK is also relevant to other professions including those advancing quantitative reasoning (QR). To illustrate, the case of PCK for teaching QR is considered. Those in fields such as public…

A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and…

An interval estimation procedure is discussed that can be used to evaluate the probability of a particular response for a binary or binary scored item at a pre-specified point along an underlying latent continuum. The item is assumed to: (a) be part of a unidimensional multi-component measuring instrument that may contain also polytomous items,…

Most of the social science research is based on the implied assumption that measurement error is the same across key socio-demographic groups and all differences in key statistics of interest are real. Nevertheless, there is evidence that this is not the case. In this paper, the authors tackle this important topic by investigating if data quality…

We provide tools for identification and exploration of data with very large variability having power law tails. Such data describe extreme features of processes such as fire losses, flood, drought, financial gain/loss, hurricanes, population of cities, among others. Prediction and quantification of extreme events are at the forefront of the…

Contextual, identity, and cultural factors are not only associated with student outcomes but can also serve to moderate the effects of interventions. However, the conventional analysis of moderation commonly used in school psychology is subject to the selection bias potentially introducing bias into estimated moderator effects. This article…

This tutorial uses publicly available data from drug makers and the Food and Drug Administration to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates with a Bayesian framework. Under the classical approach, there is no probability associated with a parameter, and the meaning of confidence intervals can be…

In a randomized controlled trial (RCT), some subjects assigned to the treatment condition may not fully comply. Often there is interest in the effect of the treatment within the "principal stratum" of subjects who would comply if assigned to treatment. However, it is unknown which control subjects would have complied if treated and which…

Mixture models have been developed to enable detection of within-subject differences in responses and response times to psychometric test items. To enable mixture modeling of both responses and response times, a distributional assumption is needed for the within-state response time distribution. Since violations of the assumed response time…

Transition metrics, which quantify the propensity for one event to follow another, are often utilized to study sequential patterns of behaviors, emotions, actions, and other states. However, little is known about the conditions in which application of transition metrics is appropriate. We report on two experiments in which we simulated sequences…