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…

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…

The ability estimation procedure is one of the most important components in a computerized adaptive testing (CAT) system. Currently, all CATs that provide K-12 student scores are based on the item response theory (IRT) model(s); while such application directly violates the assumption of independent sample of a person in IRT models because ability…

We calculate the number of subgroups in a direct product of finite cyclic groups by applying the fundamental theorem of finite abelian groups and a well-known structure theorem due to Goursat. We also suggest ways in which the results can be generalized to a direct product of arbitrary finite groups.

The Josephson effect, the 50th anniversary of which will be celebrated in 2012, remains one of the most spectacular manifestations of quantum mechanics in all of experimental science. It was first predicted in 1962 and then experimentally verified in 1963. At its most fundamental level the Josephson effect is nothing more than the electronic…

Conventional application of these two calculus staples is stretched here, somewhat recreationally, but also to raise solid questions about the role of limit interchange in analysis--without, however, delving any deeper than first-year Calculus.

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.