For ease of instruction in the classroom, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. Likewise, the Kruskal-Wallis statistic may be rewritten in terms of pairwise differences in individual…

Students often learn about measurement uncertainty as an isolated topic, with a focus on generalizable strategies to manage uncertainty in scientific investigation. In this study, we report and analyze a case of emergent learning about measurement and uncertainty, in which students in a Chinese elementary school science class explored and…

The RizbA scale combines psychometrics and art theory and enables a measurement of pictorial expression. This study explores its factor structure and a potential gap between theory and empirics. A sample of 275 pictorial works by artists and nonprofessionals was rated by 179 art experts. Three CFA path models were specified: models A and B based…

With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy's integral theorem. The analysis of the mathematical activity was carried out through the identification of the…

The diversity of scientific methods has received increasing attention in the field of science education. This paper aimed to investigate how preservice chemistry teachers perceive scientific methods and their diversity. Based on the theoretical framework of Brandon's Matrix and previous research, two tasks (i.e., Task 1 "understanding of the…

Researchers are often inclined to test agreement or discrepancy hypotheses using difference scores. This commentary explains 2 mathematical-statistical principles underlying associations with difference scores and 2 conceptual-interpretation problems that make difference scores inappropriate for testing such hypotheses. The commentary provides…

We first review existing literature on cumulative logit models along with various ways to test the parallel lines assumption. Building on the traditional frequentist framework, we introduce a method of Bayesian assessment of null values to provide an alternative way to examine the parallel lines assumption using highest density intervals and…

Humans actively seek information to reduce uncertainty, providing insight on how our decisions causally affect the world. While we know that episodic memories can help support future goal-oriented behaviors, little is known about how hypothesis testing during exploration influences episodic memory. To investigate this question, we designed a…

Multivariate analysis of variance (MANOVA) is widely used to test the null hypothesis of equal multivariate means across 2 or more groups. MANOVA rests upon an assumption that error terms are independent of one another, which can be violated if individuals are clustered or nested within groups, such as schools. Ignoring such nesting can result in…

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,…

Criteria are briefly proposed for final conclusions, research problems, and research hypotheses in quantitative research. Moreover, based on a proposed definition of applied and basic/general research, it is argued that (1) in applied quantitative research, while research problems are necessary, research hypotheses are unjustified, and that (2) in…

Birth weight is a robust predictor of valued life course outcomes, emphasizing the importance of prenatal development. But does birth weight act as a proxy for environmental conditions in utero, or do biological processes surrounding birth weight themselves play a role in healthy development? To answer this question, we leverage variation in birth…

We tested the educational effectiveness of an inquiry-guided approach (Lee et al., 2004; Prince & Felder in "Journal of Engineering Education, 95," 123-138, 2006) to teaching a possible outcome of statistical hypothesis testing known as type 1 error. The approach consisted of showing participants an animated space exploration video.…

Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based upon several common approaches for handling dependent effect sizes. In a Monte Carlo simulation, we…

Purpose: This article provides a tutorial introduction to ordinal pattern analysis, a statistical analysis method designed to quantify the extent to which hypotheses of relative change across experimental conditions match observed data at the level of individuals. This method may be a useful addition to familiar parametric statistical methods…