Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

A readily applicable procedure is discussed that allows evaluation of the discrepancy between the popular coefficient alpha and the reliability coefficient of a scale with second-order factorial structure that is frequently of relevance in empirical educational and psychological research. The approach is developed within the framework of the…

It can readily be demonstrated that when a low frequency alternating voltage is applied to an iron-core coil the impedance is much higher than the direct current resistance of the coil. To understand how the high level of impedance arises it is necessary to explain how magnetic and electrical induction give rise to a current in the coil that…

Mplus is a powerful latent variable modeling software program that has become an increasingly popular choice for fitting complex item response theory models. In this short note, we demonstrate that the two-parameter logistic testlet model can be estimated as a constrained bifactor model in Mplus with three estimators encompassing limited- and…

Lagrange multiplier (LM) or score tests have seen renewed interest for the purpose of diagnosing misspecification in item response theory (IRT) models. LM tests can also be used to test whether parameters differ from a fixed value. We argue that the utility of LM tests depends on both the method used to compute the test and the degree of…

Since the 1970s, catalogs of protest events have been at the heart of research on social movements. To measure how protest changes over time or varies across space, sociologists usually count the frequency of events, as either the dependent variable or a key independent variable. An alternative is to count the number of participants in protest.…

Public financing of privately provided child care can allow for access to these services in places where public provision and capacity are low. However, the mechanisms of subsidy delivery will affect who benefits, and the overall cost-effectiveness of such subsidies. This paper sets out an ex-ante simulation model for estimating the benefit…

Open-ended problems are a very effective tool for engaging student interest. In this paper, we report a physics activity that provides insight into the lifestyle of theropod dinosaurs. This activity generates great enthusiasm among the students since virtually everyone is interested in dinosaurs. In the spirit of the "spherical cow"…

As research on mediation has grown, so too has interest in identifying ways to assess the size of indirect effects in a mediation analysis. One such estimate -- the ratio of the indirect effect to the total effect (P[subscript M]) -- was tested in a sample of 21,297 children from the Early Childhood Developmental Study. Results showed that the two…

A factor that complicates the posting of the journal entries related to the issue of bonds is that the amount of money received by the issuing company may be different from the face value of the bond. If the bond stated rate is higher than the market interest rate at the time of issue of the bond, the company can sell the bond at a premium; on the…

Propensity and prognostic score methods are two statistical techniques used to correct for the selection bias in nonexperimental studies. Recently, the joint use of propensity and prognostic scores (i.e., two-score methods) has been proposed to improve the performance of adjustments using propensity or prognostic scores alone for bias reduction.…

This paper introduces a percentage activity based on the context of "Black Friday" discounts. The aim of the study was to reveal the existing and new conceptions of the 7th grade students regarding the topic of percentage calculation. The activity was designed considering the students' prior knowledge in the concept of "Ratio and…

The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels--one for the responses and one for the response times--that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a…

Digital literacy is a need for our current society. In Mexico, digital incursion programs are barely implemented, which represents an educational delay compared to other countries that have faced the need to integrate the teaching of digital skills, in a wide range of educational levels. This paper presents a learning environment of Computational…

Estimating the effects of randomized experiments and, by extension, their mediating mechanisms, is often complicated by treatment noncompliance. Two estimation methods for causal mediation in the presence of noncompliance have recently been proposed, the instrumental variable method (IV-mediate) and maximum likelihood method (ML-mediate). However,…