Propensity score methods account for selection bias in observational studies. However, the consistency of the propensity score estimators strongly depends on a correct specification of the propensity score model. Logistic regression and, with increasing popularity, machine learning tools are used to estimate propensity scores. We introduce a…

The ability of universities and colleges to predict the success of admitted students continues to be a key concern of higher education officials. Apart from a desire to see students have successful academic careers, there is also the fiscal reality of greater tuition revenues providing needed support for university budgets. Using administrative…

Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured…

Unavoidable sample size issues beset psychological research that involves scarce populations or costly laboratory procedures. When incorporating longitudinal designs these samples are further reduced by traditional modeling techniques, which perform listwise deletion for any instance of missing data. Moreover, these techniques are limited in their…

The impact of misspecifying covariance matrices at the second and third levels of the three-level model is evaluated. Results indicate that ignoring existing covariance has no effect on the treatment effect estimate. In addition, the between-case variance estimates are unbiased when covariance is either modeled or ignored. If the research interest…

The purpose of this study is to evaluate the extent to which item response theory (IRT) proficiency estimation methods are robust to the presence of aberrant responses under the "GRE"® General Test multistage adaptive testing (MST) design. To that end, a wide range of atypical response behaviors affecting as much as 10% of the test items…

Propensity score estimation plays a fundamental role in propensity score matching for reducing group selection bias in observational data. To increase the accuracy of propensity score estimation, the author developed a bootstrap propensity score. The commonly used propensity score matching methods: nearest neighbor matching, caliper matching, and…

The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

This is the latest in a series of polls sponsored by Phi Delta Kappa International with the Gallup organization. Some important findings of this year's poll include: About half of us believe teacher unions are hurting public education, but we're more likely to support teacher union leaders than governors in disputes over teacher collective…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…