Developed an empirical Bayes enhancement to Mantel-Haenszel (MH) analysis of differential item functioning (DIF) in which it is assumed that the MH statistics are normally distributed and that the prior distribution of underlying DIF parameters is also normal. (Author/SLD)

Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions, especially those related to transfer to other distributions. Results are formulated as a series of theorems and corollaries that apply to…

Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…

Derives the asymptotic normal distribution of the maximum likelihood estimator of Cronbach's alpha (under normality) for the case when no assumptions are made about the covariances among items. Also considers the asymptotic distribution for the special case of compound symmetry and when compared to the exact distribution. (Author/SLD)

Derives approximations to the distributions of goodness-of-fit indexes in structural equation modeling with the assumption of multivariate normality and slight misspecification of models. Also derives an approximation to the asymptotic covariance matrix for the fit indexes by using the delta method and develops approximations to the densities of…

Compared the analysis of variance (ANOVA) "F" and several nonparametric competitors for two-way designs for empirical alpha and power through simulation. Results suggest the ANOVA "F" suffers from conservative alpha and power for the mixed normal distribution, but is generally recommended. (Author/SLD)

Methods for calculating confidence intervals for the mean are reviewed for the case where the data come from a log-normal distribution. In a simulation study it is found that a variation of the method suggested by Cox works well in practice. An approach based on Generalized confidence intervals also works well. A comparison of our results with…

The data illustrate outliers that are not mistakes and not observations that are unusually high or low. The reasons for them are all interesting historically. They illustrate that "outliers" need not be errors but may instead be particularly interesting cases. The data also illustrate that different data displays may differ in their ability to…

Given the extent to which our society values education, it is perplexing to learn that we continue to struggle to provide all children, especially homeless children, an adequate education. This troubling issue is the focus of this paper. Specifically, this paper will center around two basic questions; 1) what has the legal system done to ensure…

A special but common type of scenario is one in which a company has a promotion that is designed to make the customer purchase more of their product than they otherwise might. Although this can be aimed specifically at children, it really applies to all persons. The basic premise is that the company issues a "set" of different items or…

The authors describe and illustrate 6 factors that affect the size of a Pearson correlation: (a) the amount of variability in the data, (b) differences in the shapes of the 2 distributions, (c) lack of linearity, (d) the presence of 1 or more "outliers," (e) characteristics of the sample, and (f) measurement error. Also discussed are ways to…

This paper presents an expository development of James-Stein estimation with substantial emphasis on exact results for nonnormal location models. The themes of the paper are: (1) the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; (2) the amount of…

The correlation coefficient is an integral part of many other statistical techniques (analysis of variance, t-tests, etc.), since all analytic methods are actually correlational (G. V. Glass and K. D. Hopkins, 1984). The correlation coefficient is a statistical summary that represents the degree and direction of relationship between two variables.…

Outliers, extreme data values relative to others in a sample, may distort statistics that assume internal levels of measurement and normal distribution. The outlier may be a valid value or an error. Several procedures are available for identifying outliers, and each may be applied to errors of prediction from the regression lines for utility in a…

Information loss occurs when continuous data are grouped in discrete intervals. After calculating the squared correlation coefficients between continuous data and corresponding grouped data for four population distributions, the effects of population distribution, number of intervals, and interval width on information loss and recovery were…