The posterior distribution of the bivariate correlation is analytically derived given a data set where "X" is completely observed, but "Y" is missing at random for a portion of the sample. Interval estimates of the correlation are constructed from the posterior distribution in terms of the highest density regions. (SLD)

This paper demonstrates that two major tests for two-by-two tables, Fisher's exact and Pearson's chi-square tests, are highly related from a Bayesian perspective. A formal similarity is demonstrated in small samples, and reasons for the relationship are discussed. (SLD)

A general delta method is described for computing the standard error (SE) of a chain of linear equations. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. Computer simulations demonstrate the method. (SLD)

Proposes a mathematical model to explain the observed concentration or diversity of nominal classes in information retrieval systems. The Lorenz Curve is discussed, Information Production Process (IPP) is explained, and a heuristic explanation of circumstances in which the model might be used is offered. (30 references) (LRW)

This article describes the theoretical distribution of optima arising from two-category univariable optimal discriminant analysis (UniODA) of continuous random data for a one-tailed (directional) hypothesis. Directional UniODA is illustrated through an investigation of the relationship between depression and brain monoamine turnover. (SLD)

Two ideal-point probabilistic choice models from the external analysis of preferences are presented that allow for more flexible distributions of ideal-points. The first extends the probit model of W. Kamakura and R. Srivastava. The second is based on simplifying assumptions that lead to a multidimensional histogram of ideal-points. (SLD)

The power functions of Student t tests performed on initial scores, ordinary ranks, 3 kinds of modular ranks, and dichotomies were investigated for 1 normal and 3 nonnormal distributions using 2 samples of 26 simulated scores each. Advantages of extending the rank transformation concept are discussed. (SLD)

The normality of number distributions generated by various random-number generators were studied, focusing on when the random-number generator reached a normal distribution and at what sample size. Findings suggest the steps that should be followed when using a random-number generator in a Monte Carlo simulation. (SLD)

It is argued that outlier-prone distributions reduce the power of nonparametric tests, but power can be restored through procedures usually associated with parametric tests. Computer simulation is used to show how an outlier detection and downweighting procedure augments the power of the t-test and the Wilcoxon-Mann-Whitney test. (SLD)

Proposes a marginal Bayesian estimation procedure to improve item parameter estimates for the three parameter logistic model. Computer simulation suggests that implementing the marginal Bayesian estimation algorithm with four-parameter beta prior distributions and then updating the priors with empirical means of updated intermediate estimates can…

This article demonstrates that the lower bound for the most deviant Z score and the upper bound for the sample standard deviation are attained simultaneously.

Of California's 6.3 million public school students in 2006-07, 1.6 million (25%) were considered English learners (EL). Although the vast majority of ELs in the state are Spanish-speaking, more than 50 languages are represented in the state's EL population. English learners are distributed throughout the state and across grade levels, with the…

Using fiscal data provided by the finance office of the school district, and personnel data obtained from the California Basic Education Data System maintained by the California Department of Education (CDE), the authors present analyses to provide a foundation for local policymakers that may be used to assess whether there are inequities in the…

In this issue's "Classroom Notes" section, the following papers are described: (1) "Sequences of Definite Integrals" by T. Dana-Picard; (2) "Structural Analysis of Pythagorean Monoids" by M.-Q Zhan and J. Tong; (3) "A Random Walk Phenomenon under an Interesting Stopping Rule" by S. Chakraborty; (4) "On Some Confidence Intervals for Estimating the…

A simple, direct condition is formulated for determining the mode(s) of a probability mass function. This condition is then applied to the Poisson and hypergeometric mass functions.