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,…

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…

Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in place of their parametric counterparts when there is evidence or belief that the assumptions of the parametric test are not met (i.e., normally distributed dependent variables). An underlying and often unattended to assumption of nonparametric…

Children acquiring languages with noun classes (grammatical gender) have ample statistical information available that characterizes the distribution of nouns into these classes, but their use of this information to classify novel nouns differs from the predictions made by an optimal Bayesian classifier. We use rational analysis to investigate the…

We present three strategies to replace the null hypothesis statistical significance testing approach in psychological research: (1) visual representation of cognitive processes and predictions, (2) visual representation of data distributions and choice of the appropriate distribution for analysis, and (3) model comparison. The three strategies…

Purpose: The aim of the paper is to evaluate how advisory services stimulate the adoption of rural development policies (RDP) aiming at value creation. Design/methodology/approach: By linking the use of agricultural extension services (AES) to policies for value creation, we will put forward an empirical analysis in Italy, with the aim of…

This paper introduces a dataset and associated analysis of the scores of National Football League (NFL) games over the 2012, 2013, and first five weeks of the 2014 season. In the face of current media attention to "lopsided" scores in Thursday night games in the early part of the 2014 season, t-test results indicate no statistically…

Researchers occasionally have to work with an extremely small sample size, defined herein as "N" less than or equal to 5. Some methodologists have cautioned against using the "t"-test when the sample size is extremely small, whereas others have suggested that using the "t"-test is feasible in such a case. The present…

This paper examines the use of a randomization-based activity to introduce the ANOVA F-test to students. The two main goals of this activity are to successfully teach students to comprehend ANOVA F-tests and to increase student comprehension of sampling distributions. Four sections of students in an advanced introductory statistics course…

Whenever you think you have an idea of how something works, you have a mental model. That is, in effect, a layman's way of talking about having an hypothesis. The hypothesis needs to be tested for how closely it fits reality--and reality is the data collected from an experiment. So the data is collected on the few and compared with a few…

We use quantile treatment effects estimation to examine the consequences of the random-assignment New York City School Choice Scholarship Program across the distribution of student achievement. Our analyses suggest that the program had negligible and statistically insignificant effects across the skill distribution. In addition to contributing to…

Among some gifted education researchers, advocates, and practitioners, it is sometimes believed that there is a larger number of gifted people in the general population than would be predicted from a normal distribution (e.g., Gallagher, 2008; N. M. Robinson, Zigler, & Gallagher, 2000; Silverman, 1995, 2009), a belief that we termed the…

The purpose of this study was to inform the deliberations of a policymakers' working group by investigating what key actors in the materials' marketplace are doing to align digital and print-based materials with the Australian Curriculum and what steps need to be taken to deliver aligned materials to schools. Content analysis method was used to…

Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of…

Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we…