This paper walks the reader through a simple mathematical characterization of the popular children's game, "Chutes and Ladders," focusing primarily on Monte Carlo simulation. The focus is then shifted to the board game "No Te Enojes" in order to analyze the implications of the introduction of strategy. The presence of strategy…

Monte Carlo simulations for uncertainty propagation take as inputs the uncertainty distribution for each variable and an equation for the calculation of a desired quantity. The desired quantity is then calculated by randomly drawing from the specified uncertainty distributions of the input variables. This calculation is then repeated many times…

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…

Problems requiring numerical solutions of differential equations or the use of agent-based modeling are presented for use in a course on mass transfer. These problems were solved using the popular technical computing language MATLABTM. Students were introduced to MATLAB via a problem with an analytical solution. A more complex problem to which no…

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…

This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are…

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…

Many imputation techniques and imputation software packages have been developed over the years to deal with missing data. Different methods may work well under different circumstances, and it is advisable to conduct a sensitivity analysis when choosing an imputation method for a particular survey. This study reviewed about 30 imputation methods…

Describes how microcomputers can perform very demanding/large-scale physics calculations at speeds not much slower than those of modern, full-size computers. Among the examples provided are a Monte Carlo simulation of the three-dimensional Ising model and a program (for the Apple microcomputer) using the time-independent Schrodinger Equation. (JN)

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…

Discusses making a computer-simulated rainbow using principles of physics, such as reflection and refraction. Provides BASIC program for the simulation. Appends a program illustrating the effects of dispersion of the colors. (YP)

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…

Discussion of the use of computer simulation in the social sciences highlights types of simulation strategies and their combinations in comprehensive simulations. The strengths and weaknesses of simulations as instructional and research tools are examined, examples are given, and design issues arising in each type are explored. (29 references)…