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…

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…

Real data are unlikely to be exactly normally distributed. Ignoring non-normality will cause misleading and unreliable parameter estimates, standard error estimates, and model fit statistics. For non-normal data, researchers have proposed a distributionally-weighted least squares (DLS) estimator to combines the normal theory based generalized…

Development of graphical methods for representing data has not kept up with progress in statistical techniques. This article presents a brief history of graphical representations of research findings and makes the case for a revival of methods developed in the early and mid-twentieth century, notably ISOTYPE and Chernoff's faces. It resurrects and…

The ability to interpret and compare data distributions is an important educational goal. Inherent in the statistical concept of distribution is the need to focus not only on individual data points or small groups of data points (so-called local view), but to perceive a distribution as a whole, allowing to recognize global features such as center,…

Data in social and behavioral sciences typically contain measurement errors and do not have predefined metrics. Structural equation modeling (SEM) is widely used for the analysis of such data, where the scales of the manifest and latent variables are often subjective. This article studies how the model, parameter estimates, their standard errors…

Data in social and behavioral sciences typically contain measurement errors and do not have predefined metrics. Structural equation modeling (SEM) is widely used for the analysis of such data, where the scales of the manifest and latent variables are often subjective. This article studies how the model, parameter estimates, their standard errors…

The purpose of this study is to illustrate the use of functional data analysis (FDA) as a general methodology for analyzing person response functions (PRFs). Applications of FDA to psychometrics have included the estimation of item response functions and latent distributions, as well as differential item functioning. Although FDA has been…

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).

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

Model uncertainty is pervasive in social science. A key question is how robust empirical results are to sensible changes in model specification. We present a new approach and applied statistical software for computational multimodel analysis. Our approach proceeds in two steps: First, we estimate the modeling distribution of estimates across all…

Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…

Teacher churning likely harms student achievement. However, the phenomenon of within-school grade-level teacher reassignments is understudied. The current study provides descriptive evidence on the frequency and predictors of within-school teacher grade switching using both longitudinal administrative data from Michigan and nationally…

The number of increases a particular stock makes over a fixed period follows a Poisson distribution. This article discusses using this easily-found data as an opportunity to let students become involved in the data collection and analysis process.

Using a data set exclusively prepared for and licensed to them by the College Board, the authors examined the growth of the Advanced Placement program in foreign languages and overall trends in regard to the number of candidates who sat for the foreign language exams, their gender, their scores, and their ethnicity over the 36-year period covering…