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…

Randomized experiments are commonly used to evaluate the effectiveness of educational interventions. The goal of the present investigation is to develop small-sample corrections for multiple contrast hypothesis tests (i.e., F-tests) such as the omnibus test of meta-regression fit or a test for equality of three or more levels of a categorical…

When using existing technology, it can be hard or impossible to determine whether two structural equation models that are being considered may be nested. There is also no routine technology for evaluating whether two very different structural models may be equivalent. A simple nesting and equivalence testing (NET) procedure is proposed that uses…

Selectivity problems are discussed in terms of a general model that is estimated by the maximum likelihood method. Both single-group and multiple-group analyses are considered. An extension of the general model to latent variable models is discussed. (Author/PN)

The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood factor analysis. Simulations are performed in which t-statistics based upon these jackknife estimates of the standard errors are computed.…

Examined the performance of a recently available full information maximum likelihood (FIML) estimator in a multiple regression model with missing data using Monte Carlo simulation and considering the effects of four independent variables. Results indicate that FIML estimation was superior to that of three ad hoc techniques, with less bias and less…

The application of latent trait theory to classroom tests necessitates the use of small sample sizes for parameter estimation. Computer generated data were used to assess the accuracy of estimation of the slope and location parameters in the two parameter logistic model with fixed abilities and varying small sample sizes. The maximum likelihood…

The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model, and principal axes factor analyses were performed. (Author/LMO)

The paper reviews the research on design and operation of research libraries sponsored by the Purdue University Libraries and the Purdue School of Industrial Engineering. The use of mathematical models in library operations research is discussed. Among the mathematical methods discussed are marginal analysis or cost minimization, computer…

Presents suggestions for making statistical topics interesting and relevant in the classroom. For each of the topics, a general discussion is followed by a suggested teaching sequence with specific activities and examples. (PK)

Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…

Computer generated data are used to show that Slinde and Linn's criticism of the usefulness of the Rasch model for equating (EJ 189 585) may have been the result of an artifact produced by the manner in which the samples were chosen in their study. (CTM)

Statistical significance is misused in educational and psychological research when it is applied as a method to establish the reliability of research results. Other techniques have been developed which can be correctly utilized to establish the generalizability of findings. Methods that do provide such estimates are known as invariance or…