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…

This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple…

Missing data are a pervasive problem in data analysis. Three common methods for addressing the problem are (a) complete-case analysis, where only units that are complete on the variables in an analysis are included; (b) weighting, where the complete cases are weighted by the inverse of an estimate of the probability of being complete; and (c)…

Subjects with initially extreme observations upon remeasurement are found closer to the population mean. This tendency of observations toward the mean is called regression to the mean (RTM) and can make natural variation in repeated data look like real change. Studies, where subjects are selected on a baseline criterion, should be guarded against…

In statistics classes, the central limit theorem has been demonstrated using simulation-based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real-data-based simulations are here…

Teaching and learning undergraduate statistics has been a most challenging task for undergraduate psychology majors (Salkind, 2017). A seasoned statistics instructor consulted with a seasoned instructional designer on a method to improve a particularly demanding course using a performance improvement approach to address learning difficulties she…

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…

A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that…

This paper introduces an approach that uses latent class analysis to identify cut scores (LCA-CS) and categorize respondents based on context scales derived from largescale assessments like PIRLS, TIMSS, and NAEP. Context scales use Likert scale items to measure latent constructs of interest and classify respondents into meaningful ordered…