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…

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach,…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

Growth curve models are widely used for investigating growth and change phenomena. Many studies in social and behavioral sciences have demonstrated that data without any outlying observation are rather an exception, especially for data collected longitudinally. Ignoring the existence of outlying observations may lead to inaccurate or even…

The author responds to the article by Warne, Godwin, and Smith (2013) on the question of whether there are more gifted people than would be expected in a Gaussian normal distribution. He asserts that the answer to this question is yes, based on (a) data that he and his colleagues have collected, (b) data that are already available and quoted by…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

The quantal hypothesis is central to the modern understanding of how a neurotransmitter is released from synapses. This hypothesis expresses that a neurotransmitter is packaged together in quanta that are released probabilistically. The experiments that led to the quantal hypothesis are often related in introductory neuroscience textbooks, but…

The aim of this paper is to discuss different approaches to the quality (or uncertainty) of measurement data considering both historical examples and today's students' views. Today's teaching of data analysis is very much focussed on the application of statistical routines (often called the "Gaussian approach" to error analysis). Studies on…

In many surveys, the data comprise a large number of categorical variables that suffer from item nonresponse. Standard methods for multiple imputation, like log-linear models or sequential regression imputation, can fail to capture complex dependencies and can be difficult to implement effectively in high dimensions. We present a fully Bayesian,…

Measures of classroom environments have become central to policy efforts that assess school and teacher quality. This has sparked a wide interest in using multilevel factor analysis to test measurement hypotheses about classroom-level variables. One approach partitions the total covariance matrix and tests models separately on the…

This study investigated the levels of possession of science process skills by final year Nigerian Certificate in Education (NCE) Students in colleges of Education in South-Eastern States of Nigeria. The skills that were assessed were observation, experimentation, measurement, communication, and inference. The research was guided by five research…

Considerable discrepancies between the mean and median often occur in data sets that are skewed left, skewed right, or have other unusual features. In such cases, it is important to analyze the data and context carefully to decide how best to describe centers of distributions. The importance of this type of statistical thinking is acknowledged in…

Grades at US colleges and universities have increased precipitously over the last 50 years, suggesting that their signalling power has become attenuated. Moreover, average grades have risen disproportionately in some departments, implying that weak students in departments with high grades may obtain better class ranks than strong students in…

Is the t test statistic for the Pearson Product Moment Correlation Coefficient robust to errors of the second kind? This investigation indirectly measured the effects of power through a type 2 error rate robustness study. The results were revealing. [The dissertation citations contained here are published with the permission of ProQuest LLC.…

Prior research investigating PSTs' statistical thinking is sparse, yet teacher educators need to know how best to prepare future teachers for their work and given the increasing importance of STEM education we need teachers who are capable of preparing students at an early age to think about data. In this paper we share the results from a study…