Iowa State University

Educators, in general, and teachers of statistical methods, in particular, have recognized the value to students of active learning. This has lead to the wide use of assignments in statistical methods courses where students use modern commercial statistical software and computing equipment to analyze real or realistic data. Data analysis assignments enable most students to master the mechanics of data analysis. The amount of experience that a student can get with such assignments is, however, limited. Thus, a sizable proportion of students have difficulty grasping some of the many important concepts that are introduced in these courses. This is particularly so for concepts that require visualizing in more than two or three dimensions (e.g., multiple regression surfaces) or that require theory beyond the mathematical abilities of the students (e.g., large-sample approximate sampling distributions). Nevertheless, these concepts are important for effective modeling and data analysis and instructors should focus on them. By using modern computing technology, it is possible to supplement standard data analysis assignments and algebraic (numeric) derivations (illustrations) and have students become actively involved in the learning of important statistical concepts. The learning experience can be enhanced by giving students additional statistical "experiences" by using combinations of carefully designed and implemented multiple simulations and high resolution dynamic graphics to illustrate key ideas.

We intend to develop approximately 30 easy-to-use instructional software modules that will go beyond standard data analysis methodology. These modules will illustrate concepts, provide important insights, and lead to more meaningful experiences and assignments with real or realistic problems of data analysis and inference. They will use a combination of state-of-the-art workstations, statistical programming languages, high resolution color graphics, simulation, and a highly interactive user interface. Many modules will be used in more than one course. Undergraduate courses to be affected by this program include: applied time series, statistical research methods (regression analysis and analysis of variance), multivariate analysis, quality control, and experimental design, as well as some service courses. This approach should lead to more meaningful experiences and assignments with real or realistic problems of data analysis and inference, reinforcing the important concepts.

TABLE 1: Proposed Computer Modules to be Constructed and Used to Illustrate Important Statistical Concepts to Undergraduate Students

================================================================================ Responsible Short Name Person Course(s) ------------------------------------------- ----------- ------------------ Module 1: Basic Statistics (Likely platform Splus, except Lisp-Stat for 10.) 1. Exploring the use of probability plots Meeker 328,401,451,481 2. Interpretation of confidence intervals Meeker 101,104,227,305, 328,401 3. Interpretation of prediction intervals Meeker 227,305,328,401,451 4. Interpretation of tolerance intervals Meeker 231,305,361 5. Sampling distributions: Stephenson 101,104,227,305,401 one-sample t statistic 6. Sampling distributions: Stephenson 101,104,227,305,401 two-sample t statistic 7. Sampling distributions: sample proportion Stephenson 101,104,227 8. Sampling distributions: sample variance Stephenson 101,104,227 9. Effect of sample size and significance Kaiser 101,104,227 level on test power 10. The effect of transformations on Marasinghe 328,401,451 distribution shape Module 2: Statistics in Quality Improvement (Likely platform Splus) 11. Statistical process monitoring Meeker 227,328,361 Vardeman 12. Sampling in quality assurance Vardeman 227,361 Module 3: Regression and Experimental Design (Likely platform Lisp-Stat except Splus for 14.) 13. Exploring response surface models Meeker 305,328,402 14. Blocking in experimental design Meeker 328,402 15. Randomization in experimental design Marasinghe 402 16. Interaction graphs in 2-level factorials Marasinghe 402 17. Effect of data changes Marasinghe 328,401 on influence diagnostics Kaiser 18. Effect of data changes Kaiser 328,401 on multicollinearity diagnostics Marasinghe Module 4: Nonparametric Statistics (Likely platform Splus) 19. Sampling distributions: rank-sum Groeneveld 403 statistics Stephenson 20. Sampling distribution: Spearman's rho Groeneveld 403 and Kendall's tau statistic Stephenson Module 5: Multivariate Analysis (Likely platform Splus) 21. Multivariate probability distributions Koehler 407 22. Graphical principal components Koehler 407 23. Correspondence analysis Koehler 407 Module 6: Time Series Analysis (Likely platform Splus) 24. ARIMA Models Meeker 451 25. Effect of model inadequacy on forecasts Meeker 451 26. Exploration of likelihood Meeker 451 (or sum of squares) surfaces Kaiser for nonlinear estimation Module 7: Statistical Computing (Likely platform Lisp-Stat) 27. The Monte Carlo method Marasinghe 480 28. Roundoff error in statistical computing Marasinghe 480 29. Tests for random number generators Marasinghe 480 30. Graphical methods in statistics Marasinghe 481 ================================================================================

The first faculty member listed will have primary responsibility for the module's development.

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