Simulation studies use computer-generated data to examine questions of interest that have traditionally been used to study properties of statistics and estimating algorithms. With the recent advent of powerful processing capabilities in affordable computers along with readily usable software, it is now feasible to use a simulation study to aid in…

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software "R for Statistical Computing." The author illustrates the computer simulation approach by focusing on several problems of…

This paper describes a computational exercise at undergraduate level that demonstrates the employment of Monte Carlo simulation to study the conformational statistics of flexible polymer chains, and to predict solution properties. Three simple chain models, including excluded volume interactions, have been implemented in a public-domain computer…

An approach called generalizability in item response modeling (GIRM) is introduced in this article. The GIRM approach essentially incorporates the sampling model of generalizability theory (GT) into the scaling model of item response theory (IRT) by making distributional assumptions about the relevant measurement facets. By specifying a random…

The article describes a Windows program to estimate the expected value and sampling distribution function of the adverse impact ratio for general multistage selections. The results of the program can also be used to predict the risk that a future selection decision will result in an outcome that reflects the presence of adverse impact. The method…

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

Monte Carlo simulation is a computer modeling procedure for mimicking observations on a random variable. A random number generator is used in generating the outcome for the events that are being modeled. The simulation can be used to obtain results that otherwise require extensive testing or complicated computations. This paper describes how Monte…

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

This paper investigates three methods for comparing medians rather than means in studying two independent treatment groups. The method that gave the best results is based on a normal approximation of the distribution of the sample median where the variance is estimated using results reported by Maritz and Jarrett. (Author/JAZ)

Presents sports-oriented examples (cricket and football) in which Monte Carlo methods are used on microcomputers to teach probability concepts. Both examples include computer programs (with listings) which utilize the microcomputer's random number generator. Instructional strategies, with further challenges to help students understand the role of…

This paper describes a computer simulation of Buffon's needle problem. The problem considers the probability that a needle will cross a line when the needle is thrown in a random way onto the parallel lines a certain distance apart. The paper provides the algorithm and computer program. (YP)