A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson…

In this article, we show how "Laplace Transform" may be used to evaluate variety of nontrivial improper integrals, including "Probability" and "Fresnel" integrals. The algorithm we have developed here to evaluate "Probability, Fresnel" and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals…

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal…

Estimating standard errors of estimated variance components has long been a challenging task in generalizability theory. Researchers have speculated about the potential applicability of the bootstrap for obtaining such estimates, but they have identified problems (especially bias) in using the bootstrap. Using Brennan's bias-correcting procedures…

Different formulations of thermodynamic work "w" as a pressure-volume integral are examined for a piston moving against a gas in an irreversible process. Proper expressions are obtained using the instantaneous pressure of the gas on the piston as the integrand and also using certain external pressures as the integrand. There are two common yet…

Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…

Many statistics used in the assessment of differential item functioning (DIF) in polytomous items yield a single item-level index of measurement invariance that collapses information across all response options of the polytomous item. Utilizing a single item-level index of DIF can, however, be misleading if the magnitude or direction of the DIF…

One of the most serious difficulties in the estimation of omega[subscript hierarchical] ([omega][subscript h]) has not been previously studied. Although it is true that one can impose a set of identifying constraints on one's solution to derive an estimate of [omega][subscript h] in the two-group factor case, there is the potential for introducing…

In this article, the author analyzes the cricket series match between England and Australia by applying the concept of probability. The author presents solutions for obtaining results of either team winning or both ending up in a draw in the situation of a five-match series. The author also analyzes the probability wherein the series is still…

Mental arithmetic problems were presented in one of five modes to 14 fifth-grade classrooms. Results showed no significant gains in ability to use mental arithmetic or in performance on a standardized arithmetic achievement test, but gains on a problem-solving retention test and in positive attitudes. (DT)

Studied the ability to name the days of the week for dates in the past and future (calendrical calculation) of 10 calendrical savants with Wechlser Adult Intelligence Scale scores from 50 to 97. Results suggest that although low intelligence does not prevent the development of this skill, the talent depends on general intelligence. (SLD)

This paper measures the importance of borrowing constraints on education decisions. Empirical identification of borrowing constraints is secured by the economic prediction that opportunity costs and direct costs of schooling affect borrowing-constrained and unconstrained persons differently. Direct costs need to be financed during school and…

This article discusses the calculation of odds for combined events.

This is a powerful critique of two decades of educational reform in New Zealand, from an educator who was deeply involved. It is also a provocative call for action. Bali Haque has been both a secondary school principal required to implement reform and a senior public servant in the New Zealand Qualifications Authority (NZQA) tasked with pushing…

This NCEE Technical Methods report examines how to address the problem of missing data in the analysis of data in Randomized Controlled Trials (RCTs) of educational interventions, with a particular focus on the common educational situation in which groups of students such as entire classrooms or schools are randomized. Missing outcome data are a…