This paper considers the following questions: (1) what is the relationship between the method of paired comparisons and Rasch measurement theory? (2) what is the relationship between the method of paired comparisons and graph theory? and (3) what can graph theory contribute to the understanding of Rasch measurement theory? It is specifically shown…

In this paper, six statistical tests of stochastic equality are compared with respect to Type I error and power through a Monte Carlo simulation. In the simulation, the skewness and kurtosis levels and the extent of variance heterogeneity of the two parent distributions were varied across a wide range. The sample sizes applied were either small or…

Formulae and graphs are presented allowing computation of the variances of three prototypical distributions over a finite number of categories. The uses of the variances of the maximum variance distribution, the uniform distribution and a unimodal triangular distribution to make inferences about distribution shapes are shown in several examples.…

The use of prevalence data is discussed to help find the best way to separate at-risk and not-at-risk groups. Implications of the data being distributed normally are also discussed and several examples, including one with a nonnormal distribution, are given. (Author/GK)

The normalized mean is developed and discussed as a descriptive measure of central location. The advantages of the normalized mean over the arithmetic mean, median, and trimmed mean are discussed. (Author)

Glass's estimator of effect size, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model. The exact distribution of Glass's estimator is obtained and the estimator is shown to have a small sample bias. Alternatives are proposed and discussed. (Author/JKS)

Using the characteristic curve method for dichotomously scored test items, the sampling distributions of equating coefficients were examined. Simulations indicate that for the equating conditions studied, the sampling distributions of the equating coefficients appear to have acceptable characteristics, suggesting confidence in the values obtained…

The meta-analytic method proposed by S. W. Raudenbush (1988) for studying variance heterogeneity was studied. Results of a Monte Carlo study indicate that the Type I error rate of the test is sensitive to even modestly platykurtic score distributions and to the ratio of study sample size to the number of studies. (SLD)

A simple approximation to the conditional distribution of goodness-of-fit statistics for the Rasch model is presented that is used when item difficulties are known. The approximation, which is easily programmed, gives relatively accurate assessments of conditional p-values for tests of 10 or more items. (Author/SLD)

A Monte Carlo evaluation of four test statistics for comparing dependent zero-order correlations was conducted with four sample sizes and three population distributions. Results indicate that choice of optimal test statistic depends on sample size and distribution, and predictor intercorrelation and effect size or magnitude of the…

Proposes a method for the comparative analysis of concentration in author productivity distributions; selects suitable measures, Gini's index and number of authors, for two viewpoints regarding productivity; discusses statistical peculiarities of author productivity data; and explains developmental profiles which take into account sample size…

Compared the nominal and empirical null distributions of the standardized log-likelihood statistic for polytomous items for paper-and-pencil (P&P) and computerized adaptive tests (CATs). Results show that the empirical distribution of the statistic differed from the assumed standard normal distribution for both P&P tests and CATs. Also…

Presents a probability model of the occurrence of index terms used to derive discrete distributions which are mixtures of Poisson and negative binomial distributions. These distributions give better fits than the simpler Zipf distribution, have the advantage of being more explanatory, and can incorporate a time parameter if necessary. (25…

Demonstrates the use of the Waring distribution as a model for the frequency distribution of scientific productivity. Methods for testing the fit at both ends of the distribution, as well as for estimating the parameters of the distribution and the total number of scientists, are outlined. (16 references) (Author/CLB)

Presents a system of software and analysis for the development of mathematical models designed to explain the structure in large bibliographic data sets. The discussion covers the goodness of fit obtained in testing and replications, and the implications for the control of large information systems. (six references) (CLB)