Four experiments involving 180 undergraduates evaluated the effectiveness of computer graphics in improving estimates for algebra word problems. Variations in the simulation resulted in successful and unsuccessful programs as measured by the frequency with which students improved their estimates. Quality of feedback to students while learning is…

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

Illustrates how to use computer simulation models in statistics to study the quality of an estimation procedure and concurrently the subtle concepts of randomness and convergence. Special emphasis is given to the use of graphical representations. (MKR)

A reparameterization of a latent class model is presented to classify and scale nomial and ordered categorical choice data simultaneously. The model extension represents a nonhomogeneous population as a mixture of homogeneous subpopulations. Simulated data and data from a magazine preference survey of 347 college students illustrate the model.…

A normally distributed data set of 1,000 values--ranging from 50 to 150, with a mean of 50 and a standard deviation of 20--was created in order to evaluate the bootstrap method of repeated random sampling. Nine bootstrap samples of N=10 and nine more bootstrap samples of N=25 were randomly selected. One thousand random samples were selected from…

A model for constrained computerized adaptive testing is proposed in which the information in the test at the ability estimate is maximized subject to a large variety of possible constraints on the contents of the test. At each item-selection step, a full test is first assembled to have maximum information at the current ability estimate fixing…

Large sample standard errors of linear equating for the single-group design are derived without making the normality assumption. Two general methods based on the delta method of M. Kendall and A. Stuart (1977) are described. One method uses the exact partial derivatives, and the other uses numerical derivatives. Simulation using the beta-binomial…

Six procedures for combining sets of item response theory (IRT) item parameter estimates from different samples were evaluated using real and simulated response data. Results support use of covariance matrix-weighted averaging and a procedure using sample-size-weighted averaging of estimated item characteristic curves at the center of the ability…

Some examinees' test-taking behavior may be so idiosyncratic that their scores are not comparable to the scores of more typical examinees. Appropriateness indices, which provide quantitative measures of response-pattern atypicality, can be viewed as statistics for testing a null hypothesis of normal test-taking behavior against an alternative…

This study examined performance of a simulated computerized adaptive test that was designed to help direct the development of a medical recertification examination. The item pool consisted of 229 single-best-answer items from a random sample of 3,000 examinees, calibrated using the two-parameter logistic model. Examinees' responses were known. For…

Two studies were carried out to evaluate the quality of multidimensional item response theory (MIRT) model parameter estimates obtained from the computer program NOHARM. The purpose of the first study was to compute empirical estimates of the standard errors of the parameters. In addition, the parameter estimates were evaluated for bias and the…