In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Two-stage sampling procedures for comparing two population means when variances are heterogeneous have been developed by D. G. Chapman (1950) and B. K. Ghosh (1975). Both procedures assume sampling from populations that are normally distributed. The present study reports on the effect that sampling from non-normal distributions has on Type I error…

A rederivation of Lord's formula for estimating variance in multiple matrix sampling is presented as well as the ways Cronbach's coefficient alpha and the Spearman-Brown prophecy formula are related in this context. (Author/JKS)

L-scaling is introduced as a technique for determining the weights in weighted averages or scaled scores for T joint observations on K variables. The technique is so named because of its formal resemblance to the Leontief matrix of mathematical economics. L-scaling is compared to several widely-used procedures for data reduction, and the…

In applied and experimental research, it has been demonstrated that the extreme groups procedure is more powerful than the standard correlational approach for some values of the correlation and extreme group size. Methods are provided for using the covariance information that is usually discarded in the classical extreme groups approach.…

A method based on the Poisson approximation to the binomial distribution and on the relation between the Chi-Squared distribution and the Poisson distribution is suggested for selected use in determining the number of items and passing scores in mastery Lests. (Author/RL)

Dunnett's procedure for comparing K-1 treatments with a control is discussed within the context of three nonparametric models: those of Kruskal-Wallis, Friedman, and Cochran. (Author/MH)

Recently, C. E. McCulloch (1987) suggested a modification of the Morgan-Pitman test for comparing the variances of two dependent groups. This paper demonstrates that there are situations where the procedure is not robust. A subsample approach, similar to the Box-Scheffe test, and the Sandvik-Olsson procedure are also assessed. (TJH)

Populations of factorially simple and complex data were generated with first the oblique and orthogonal factor models, and then solutions based on special cases of the general orthomax criterion were compared on the basis of these characteristics. The results are discussed and implications noted. (DEP)

R. V. Hopkins (1982) has criticized the use of means as the unit of analysis in situations where intact groups, such as classes, rather than individuals have been randomly assigned to various treatment conditions. Instead, Hopkins advocated the use of certain analysis of variance (ANOVA) models that, as far as test for treatment effects are…

A set procedure developed in this study is useful in determining sample size, based on specification of linear contrasts involving certain formula treatments. (Author/DEP)

Three nonparametric alternatives to the parametric Bartlett test are presented for handling the K-sample equality of variance problem. The two-sample Siegel-Tukey test, Mood test, and Klotz test are extended to the multisample situation by Puri's methods. These K-sample scale tests are illustrated and compared. (Author/GDC)

In a situation where the population distribution of latent trait scores can be estimated, the ordinary maximum likelihood estimator of latent trait scores may be improved upon by taking the estimated population distribution into account. In this paper empirical Bayes estimators are compared with the liklihood estimator for three samples of 300…

A generalized variance criterion is proposed to measure efficiency in item-response-theory (IRT) models. Heuristic arguments are given to formulate the efficiency of a design in terms of an asymptotic generalized variance criterion. Efficiencies of designs for one-, two-, and three-parameter models are compared. (SLD)