Pearson's product-moment correlation can be explained by means of the probability of concordant pairs of observations on two continuous variables (ie, the order of the observations from two randomly selected individuals is the same between the two variables). The probability of concordant pairs features relatively easy computation and offers an…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

The Maxwell distribution of speeds, f(v), is the starting point for the calculation of the transport coefficients in kinetic-molecular theory. Most physical chemistry textbooks follow a path to derive f(v) similar to that used by Maxwell, which makes it difficult for students to understand its relationship with the equilibrium state of the system,…

Meta-analyses are often used to synthesize the findings of studies examining the correlational relationship between two continuous variables. When only dichotomous measurements are available for one of the two variables, the biserial correlation coefficient can be used to estimate the product-moment correlation between the two underlying…

This literature-based, classroom-tested novel innovation of educational song (with pedagogical scaffolding) may help engage students explore and address common resistant misconceptions in probability (e.g. all outcomes are equally likely) and in statistics (e.g. correlation must imply either causation or coincidence).

Few elementary students in the Commonwealth of the Northern Mariana Islands (CNMI) are scoring at grade level or higher on the ACT Aspire reading assessment. This study examined data on students who enrolled in grade 3 in a CNMI public school from 2014/15 to 2018/19 to understand their grade 3 reading performance. The study used administrative…

Connecticut is one of 29 states that require beginning teachers to complete an induction program to mitigate high turnover and lower efficacy among early-career teachers. Its two-year Teacher Education and Mentoring (TEAM) Program provides guidance to beginning teachers through several mechanisms, including five instructional modules and ongoing…

Connecticut is one of many states that implements an induction program for beginning teachers to mitigate high turnover and lower efficacy among early-career teachers. The state's Teacher Education and Mentoring (TEAM) Program requires beginning teachers to complete five instructional modules, have a certain number of contact hours with a mentor,…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

A latent variable modeling procedure is discussed that can be used to test if two or more homogeneous multicomponent instruments with distinct components are measuring the same underlying construct. The method is widely applicable in scale construction and development research and can also be of special interest in construct validation studies.…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

In this rejoinder, von Eye and DeShon discuss the decision strategies proposed in their original article ("Directional Dependence in Developmental Research," this issue), as well as the ones proposed by the authors of the commentary (Pornprasertmanit and Little, "Determining Directional Dependency in Causal Associations," this issue). In addition,…

The area of statistics is one in which teachers may be encouraged to make important links to other curriculum areas and social issues. Statistical literacy is a key component of being numerate and living as an informed citizen. The teaching of statistics provides an opportunity to inform and educate students about social issues and moral…

Research Connections conducted a comprehensive search of its collection for resources focused on the relationship between receipt of child care subsidies and employment outcomes of families receiving Temporary Assistance to Needy Families (TANF) and other low income families. From the many results, Research Connections selected a limited number of…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…