The increase in the squared multiple correlation coefficient ([delta]R[superscript 2]) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size…

This note proposes a unique solutions to find out the value of x, y and z which satisfies the equation x[superscript 2] + y[superscript 2] = z[superscript 2]. The uniqueness of the proposed formulae is to find the total number of y's and z's at a given value of x. The value of y and z can be calculated by factoring x[superscript 2] or…

Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…

When using existing technology, it can be hard or impossible to determine whether two structural equation models that are being considered may be nested. There is also no routine technology for evaluating whether two very different structural models may be equivalent. A simple nesting and equivalence testing (NET) procedure is proposed that uses…

In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…

Previous empirical studies using multiple-choice procedures have suggested that there are misconceptions about the scale of astronomical distances. The present study provides a quantitative estimate of the nature of this misconception among US university students by asking them, in an open-ended response format, to make estimates of the distances…

Three plausible assumptions of conditional independence in a hierarchical model for responses and response times on test items are identified. For each of the assumptions, a Lagrange multiplier test of the null hypothesis of conditional independence against a parametric alternative is derived. The tests have closed-form statistics that are easy to…

While both conscious and unconscious reward cues enhance effort to work on a task, previous research also suggests that conscious rewards may additionally affect speed-accuracy tradeoffs. Based on this idea, two experiments explored whether reward cues that are presented above (supraliminal) or below (subliminal) the threshold of conscious…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

In school-based randomized control trials (RCTs), a common design is to follow student cohorts over time. For such designs, education researchers usually focus on the place-based (PB) impact parameter, which is estimated using data collected on all students enrolled in the study schools at each data collection point. A potential problem with this…

The standard for measuring fuel efficiency in the U.S. has been miles per gallon (mpg). However, the Environmental Protection Agency's (EPA) switch in rating fuel efficiency from miles per gallon to gallons per hundred miles with the 2013 model-year cars leads to interesting and relevant mathematics with real-world connections. By modeling…

The order of problems presented to students is an important variable that affects learning effectiveness. Previous studies have shown that solving problems in a blocked order, in which all problems of one type are completed before the student is switched to the next problem type, results in less effective performance than does solving the problems…

The need to endow marketing graduates with skills relevant to employability grows ever more important. Marketing math and elementary financial understanding are essential employability skills, particularly given the contemporary emphasis on marketing metrics, but the evidence is that marketing graduates are often relatively weak in such skills.…

This paper examines the idea that contemporary strategic board games represent an informal, interactional context in which complex computational thinking takes place. When games are collaborative--that is, a game requires that players work in joint pursuit of a shared goal--the computational thinking is easily observed as distributed across…

For decades, researchers and practitioners have made a great deal of effort to study a variety of methods to increase parameter accuracy, but only recently can researchers start focusing on improving parameter estimations by using a joint model that could incorporate RT and students information as CI. Given that many tests are currently…