A simulation laboratory for statistics

Abstract

In this paper, we describe a general purpose data simulator, Datasim, which is useful for anyone conducting computer-based laboratory assignments in statistics. Simulations illustrating sampling distributions, the central limit theorem, Type I and Type II decision errors, the power of a test, the effects of violating assumptions, and the distinction between orthogonal and nonorthogonal contrasts are discussed. Simulations illustrating other statistical concepts-partial correlation, regression to the mean, heteroscedasticity, the partitioning of error terms in splitplot designs, and so on-ean be developed easily. Simulations can be assigned as laboratory exercises, or the instructor can execute the simulations during class, integrate the results into an ongoing lecture, and use the results to initiate class discussion of the relevant statistical concepts.Over the last several decades, instructors of statistics have experimented with the use of simulation to communicate principles of probability, sampling theory, and power analysis. Although innovative in spirit, these efforts have been hampered by the lack of a convenient method for conducting sampling experiments.1 This paper reviews a software package, called Datasim, developed specifically for this purpose (Bradley, 1988(Bradley, , 1991b. In contrast to the "coin-flipping" and "dice-rolling" labs of a previous era, Datasim is a relatively sophisticated data generator: data can be generated from discrete or continuous probability distributions, from normal or nonnormal distributions, and from populations having correlated or uncorrelated observations. Moreover, complete data sets can be generated for a variety of experimental, multivariate, and contingency table designs. Previous publications have described the basic design and capabilities of the software (Bradley, 1989a(Bradley, , 1989b, evaluated the accuracy of the random number algorithms (Bradley, Senko, & Stewart, 1990), and reviewed the methodology for conducting a simulation of a previously published study (Bradley, 1991a).Although Datasim has a number of useful applications.! the present paper focuses exclusively on computer-based laboratory assignments in which simulation is used to demonstrate one or more key concepts in statistics. The first section of the paper introduces the way in which one initializes a simulation and generates single and multiple data sets. Subsequent sections apply this method to laboratory simulationsdemonstrating the central limit theorem, Type I and Type II decision errors, the effects of violating assumptions, and orthogonal and nonorthogonal contrasts.The software described in this paper was developed by the author and is available at nominal cost from Desktop Press, 90 Bardwell 51., Lewiston, ME 04240 (phone: 207-786-4113 or 6180). Requests for reprints of this article should beaddressed to Drake R. Bradley, Department of Psychology, Bates College, Lewiston, ME 04240. Generating Simulated DataThe first step in generating simulated data is to initialize the simulation....

Evaluation of instructional software: Design considerations and recommendations

“…New software or computer-based teaching systems are regularly introduced in Behavior Research Methods, Instruments, & Computers without the requirement of even the simplest measures of efficacy (see, e.g., Bradley, 1989;Bradley, Hemstreet, & Ziegenhagen, 1992;Chute, 1986;Conn, Stafiniak, DiPasquale, & Harper, 1988;Dougherty, 1990;Isaacs, Costenbader, Reading-Brown, & Goodman, 1992;Perone, 1991;Ransdell, 1992;Ransdell & Levy, 1989;St. James, 1989;Schneider, 1988).…”

Multivariate simulation with DATASIM: The Mihal and Barrett study

“…on the Type I and Type II error rates of various statistical tests. Previous publications have described the basic design and capabilities of the software (Bradley, 1989a(Bradley, , 1989b, evaluated the accuracy of the random number algorithms (Bradley, Senko, & Stewart, 1990), reviewed the methodology for conducting a simulation of a previously published field experiment (Bradley, 1991a), and illustrated a number of laboratory simulations useful for teaching principles of sampling theory and inferential statistics (Bradley, Hemstreet, & Ziegenhagen, 1992). The present paper reviews the techniques for conducting a simulation of a multivariate study.…”

The accuracy of four approximations to noncentralF

“…As documented elsewhere (Bradley, 1989a(Bradley, , 1989b(Bradley, , 1991a(Bradley, , 1993Bradley & Fleisher, 1994;Bradley, Hemstreet, & Ziegenhagen, 1992;Bradley, Senko, & Stewart, 1990;Wright, 1993), DATASIM is a general purpose data analysis and statistical simulation program.…”