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…

This paper presents facts and figures of the international higher education. Facts reveal that the UK sells more brainpower per capita than anywhere else in the world. The UK has 1% of the world's population but undertakes 5% of the world's scientific research and produces 14% of the world's most highly cited papers (Universities UK 2010). More…

States in the U.S. are required to provide transition services to young people in special education to increase the likelihood of positive post-school outcomes (Individuals with Disabilities Education Act of 1990, IDEA, amended 1997). Fourteen years later the Individuals with Disabilities Education Improvement Act of 2004 strengthened transition…

In 3 studies, participants viewed sequences of multiattribute objects (e.g., colored shapes) appearing with varying frequencies and judged the likelihood of the attributes of those objects. Judged probabilities reflected a compromise between (a) the frequency with which each attribute appeared and (b) the ignorance prior probability cued by the…

A system of education is a unique social institution, the purpose of which is to develop and multiply human capital. Based on the education system it is possible to judge the situation in the country and society not only at the present time but also in the future. A system of education also should be seen as an ideological institution: it produces…

In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the…

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…