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.…

A reverse engineering approach to automatic item generation (AIG) was applied to a figure-based publicly released test item from the Organisation for Economic Cooperation and Development (OECD) Programme for International Student Assessment (PISA) mathematical literacy cognitive instrument as part of a proof of concept. The author created an item…

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 restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)

The concept under investigation was the reliability of estimates of mean scores of groups under various assumptions of multiple-matrix sampling when reliabilities are computed according to procedures based on generalizability theory. Four different cases were compared with respect to the generalizability coefficients depending upon whether pupils…

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…

A model for multiple choice test-taking behavior is proposed which is different from those presently used for item sampling theory. A new theory is developed, which includes a new concept to facilitate comprehension of item sampling theory, a "number-known" score distribution. A major advantage of the model is that it accommodates data from…

Investigates implications for finite and known item populations for classical test theory, and the alpha coefficient among items in paper-and-pencil testing. (Author/AG)

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…

Multiple matrix sampling is a psychometric procedure in which a set of test items is subdivided randomly into subtests of items with each subtest administered to different subgroups of examinees selected at random from the examinee population. Although each examinee receives only a proportion of the complete set of items, the statistical model…

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…