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…

The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

Designs for sequential sampling procedures that adapt to cumulative information are discussed. A familiar illustration is the play-the-winner rule in which there are two treatments; after a random start, the same treatment is continued as long as each successive subject registers a success. When a failure occurs, the other treatment is used until…

The National Assessment of Educational Progress; Second Science Assessment No-Show Study assessed the magnitude and causation of nonresponse biases. A No-Show is defined as an individual who was selected as a sample respondent but failed to be present for regular assessment of the 17-year-old group. The procedure whereby a sample of eligible…

Explicit formulas are derived for the asymptotic sampling variances and covariances of the maximum likelihood estimators for factor-analysis parameters in the special case where there is just one common factor. The effect of the number of variables on these variances and covariances is indicated. A formula is given showing to what extent the usual…

The position of the "purists" who insist on limiting data to ordinal analysis is contrasted with the "pragmatists" who treat data as interval. (Author)

The power of a statistical test is, in part, a function of the reliability of the dependable variable being analyzed. The substitution of sigma square divided by the reliability coefficient for sigma is proposed. This enables the researcher to incorporate dependent variable reliability information when determining the sample size required for a…

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)

In assessing educational equity among school districts, according to the authors, researchers should control for differences across districts in the prices of educational inputs. This paper tests a suggested index for one educational input, teacher salaries. The suggested teacher-salary index, based on a supply-and-demand model using 12 demand and…

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)

A single conceptual and theoretical framework for sampling any configuration of data from one or more population matrices is presented, integrating past designs and discussing implications for more general designs. The theory is based upon a generalization of the generalized symmetric mean approach for single matrix samples. (Author/CTM)

The equating methods and sampling designs used in the empirical studies in this special issue on the use of matched samples for test equating are described. Four requisites for equating are listed, and the invariance of equating functions requisite is identified as the focus of this issue. (SLD)

The concepts, definitions, and notation that have evolved with the development of telephone survey design methodology are discussed and presented as a unified structure. This structure is then applied to some of the more well-known telephone survey designs and alternative designs are developed. The relative merits of the different survey designs…

Least squares fitting process as a method of data reduction is presented. The general strategy is to consider fitting (linear) models as partitioning data into a fit and residuals. The fit can be parsimoniously represented by a summary of the data. A fit is considered adequate if the residuals are small enough so that manipulating their signs and…