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…

This is the fourth in a series of statistical articles for mathematics teachers. In this article, the authors discuss topics in General Mathematics in Unit 2 Topic 1 (Univariate data analysis and the statistical investigation process) and topics in Essential Mathematics, Unit 2 Topic 1 (Representing and comparing data).

This dissertation's idea began with my class notes and questions in the statistics courses I attended in my doctoral program. These notes and questions originally were about the concepts of the bell shape, statistical distribution, and hypothesis testing. They then became my inquiries of p-values because what I learned in the courses about how the…

Background: Counts are familiar outcomes in education research settings, including those involving tests of interventions. Clustered data commonly occur in education research studies, given that data are often collected from students within classrooms or schools. There is a wide array of distributions and models that can be used for clustered…

The present study aimed to remediate pre-service teachers' misconceptions about sampling distributions and to develop their conceptual understanding through the use of conceptual change texts (CCTs). The participants consisted of 84 pre-service teachers. To determine the pre-service teachers' conceptual understanding of sampling distributions, an…

Bimodal grade distributions indicate a gap in learning, where the highest quartile of students is skilful in the subject matter, but the lowest quartile is not retaining course material that demonstrates a good level of understanding. Students in the lower quartile do not necessarily have the same challenges as remedial students (i.e., those that…

Difficulties in learning (and thus teaching) statistical inference are well reported in the literature. We argue the problem emanates not only from the way in which statistical inference is taught but also from what exactly is taught as statistical inference. What makes statistical inference difficult to understand is that it contains two logics…

Both humans and non-human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate 'number sense'. However, recent simulation work has…

We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides…

Item Response Theory (IRT) models traditionally assume a normal distribution for ability. Although normality is often a reasonable assumption for ability, it is rarely met for observed scores in educational and psychological measurement. Assumptions regarding ability distribution were previously shown to have an effect on IRT parameter estimation.…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

Diagnostic accuracy studies often evaluate diagnostic tests at several threshold values, aiming to make recommendations on optimal thresholds for use in practice. Methods for meta-analysis of full receiver operating characteristic (ROC) curves have been proposed but still have deficiencies. We recently proposed a parametric approach that is based…

In social and behavioral sciences, data are typically not normally distributed, which can invalidate hypothesis testing and lead to unreliable results when being analyzed by methods developed for normal data. The existing methods of generating multivariate non-normal data typically create data according to specific univariate marginal measures…

In regression analysis courses, there are many settings in which the response variable under study is continuous, strictly positive, and right skew. This type of response variable does not adhere to the normality assumptions underlying the traditional linear regression model, and accordingly may be analyzed using a generalized linear model…

Online networks, as digital images reflecting every aspects of real world especially under the current context of information technology, have become the most massive and opulent data source these days, where vast amount of information keeps being produced and transmitted. Their rapid expansion in scale and data volume draws wide attention and…