# Development of a Modern Computing and Graphics-Based Method for Teaching Important Concepts in Undergraduate Statistics Courses

W. Q. Meeker and M. Marasinghe
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.