1. Innovative Ideas for Using Statistical Software to Teach Concepts JSM, Invited Panel Discussion August 4, 2003 Beth Chance, Cal. Poly. St. Univ. Robin Lock, St. Lawrence Univ. Deborah Nolan, Univ. of Cal, Berkeley Allan Rossman, Cal. Poly. St. Univ.

2. Outline Panelists present activities Panelists present activities  Fathom, Minitab, R, Self-developed Applets Panelists compare activities Panelists compare activities Panel discussion Panel discussion Audience questions Audience questions

3. Some Fathom Tools for Investigating Statistical Concepts Robin H. Lock Burry Professor of Statistics St. Lawrence University rlock@stlawu.edu Joint Statistics Meetings, San Francisco, August 2003

4. Three Useful Tools Interactive linked graphics Sliders Collections from collections

5. Some Minitab Tools for Investigating Statistical Concepts Allan J. Rossman Cal Poly – San Luis Obispo

6. Minitab Activities Friendly Observers: Randomization test for two-way table, significance Random Babies: Matching problem, interpretation of probability Handedness: Simulation of coverage probabilities of multiple confidence interval methods * Full versions of handouts can be found at www.rossmanchance.com/jsm03/activities

7. Minitab Activity: Friendly Observers Psychology experiment –Butler and Baumeister (1998) studied the effect of observer with vested interest on skilled performance Subjects played a video game ten times Established 70th percentile of performance score as threshold for each subject Played final game for prize, aiming to beat threshold

8. Minitab Activity: Friendly Observers 24 subjects were randomly assigned to one of two groups: –Group A: observer can also win prize –Group B: observer can not win prize Conjecture: Those whose observer did not have a vested interest would perform better –Subjects in Group B would beat threshold more often

9. Minitab Activity: Friendly Observers

10. 3/12 < 8/12 –Sample results support the conjecture, but by enough? –How often would such an extreme sample occur by chance?

11. Minitab Activity: Friendly Observers Students investigate this question through –Hands-on simulation –Student-constructed computer simulation –Mathematical model counting techniques

12. Minitab Activity: Friendly Observers Hands-on simulation: –Let 11 black cards represent “win” and 13 red cards represent “lose” –Shuffle the 24 cards and randomly deal 12 cards to represent Group A –How many of the winners/black cards were assigned to Group A? –How often do we find 3 or fewer winners in Group A if the assignment is purely random?

13. Minitab Activity: Friendly Observers 6/100

14. Minitab Activity: Random Babies Four mothers give birth to baby boys on the same night in the same hospital Hospital staff distributes babies to mothers at random Number of mothers who get the right baby –Students approximate probabilities through simulation Hands-on With technology –Enumerate sample space and determine exact probabilities

15. Minitab Activity: Random Babies Last NamesFirst Names JonesJerry MillerMarvin SmithSam WilliamsWilly

16. Minitab Activity: Handedness What proportion of students in class are left-handed? Estimate proportion of left-handers in population with 95% confidence Compare competing procedures –Under repeated random sampling, which succeeds in capturing population proportion about 95% of the time Under what conditions on n, p?

17. Minitab Activity: Handedness Conventional method: Alternative method:

18. Minitab Activity: Handedness Approximate coverage probabilities (10,000 repetitions):

19. Some Self-developed Applets for Investigating Statistical Concepts Beth L. Chance Cal Poly – San Luis Obispo

20. Self-developed Java Applets Sampling words: Simulation of sampling distributions Sampling regression lines: Simulation of sampling distributions of regression slope, intercept * Full versions of handouts can be found at www.rossmanchance.com/jsm03/activities

21. Self-developed Java Applets Activity: Sampling words –Is the sample representative of the larger population? –How do results vary from sample to sample?

22. Four score and seven years ago, our fathers brought forth upon this continent a new nation: conceived in liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground. The brave men, living and dead, who struggled here have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember, what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us, that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion, that we here highly resolve that these dead shall not have died in vain, that this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people, shall not perish from the earth.

23. Four score and seven years ago, our fathers brought forth upon this continent a new nation: conceived in liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground. The brave men, living and dead, who struggled here have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember, what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us, that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion, that we here highly resolve that these dead shall not have died in vain, that this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people, shall not perish from the earth.

24. Four score and seven years ago, our fathers brought forth upon this continent a new nation: conceived in liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground. The brave men, living and dead, who struggled here have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember, what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us, that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion, that we here highly resolve that these dead shall not have died in vain, that this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people, shall not perish from the earth. 9 2 3 5 6 4 4 10 5 Average = 5 2

25. Applet Activity: Sampling Words Students examine results for evidence of bias The population mean of all 268 words is 4.295 letters

26. Applet Activity: Sampling Words Comparing biased to random sampling

27. Applet Activity: Sampling Words What is the long-term behavior of this random sampling method? What happens if we change the sample size? Population size?

28. Self-developed Java Applets Activity: Sampling regression lines –Sample of 80 students –Cumulative GPA and hours/week studying

29. Applet Activity: Sampling Regression Lines If no relationship – GPA = 3.24 + 0(hrs/wk) How often do we see a sample slope at least this extreme?

30. Some Fathom Pros & Cons Pro: Designed for teaching concepts Con: Limited higher level analysis tools Pro: Easy to learn (point & click generation) Con: Dealing with multiple windows Pro: Easy for customizable simulations Con: Collections from collections can be tricky Pro: Interactive, dynamic linking Con: Danger of disturbing the data Pro: Infinite undo

31. More about Fathom? www. keypress.com/fathom Fathom User Group Meeting – Tonight 5:30 pm Nikko Carmel

32. Advantages of Minitab 1.Widely used and powerful data analysis tool 2.Not separate software tool to be learned 3.Can be used in subsequent statistics courses 4.Relatively flexible and extendable 5.Relatively easy-to-learn 6.Students can learn/apply some programming skills

33. Disadvantages of Minitab 1.More tempting for students to focus on software/programming and not concepts 2.Not as clear a link to context/activity 3.Not as interactive or dynamic 4.Not as visually appealing or effective

34. Other Applet Features Dragging, shading, color-coding Data analysis, probability calculations, inference calculations Predict and test

35. Advantages of Self-developed Applets Portability! Very visual and interactive, see effects immediately Appeals to students’ sense of “play,” easy to begin use Can make clear connection to tactile simulation, reducing level of abstraction Collaboration between statistics teacher and programmer –Ability to modify based on classroom use

36. Disadvantages of Applets Can be more difficult to match existing course materials –May not give a consistent look and feel Can be more difficult to extend exploration –More instructor-led investigations, no “help” button Will probably also need a stand alone statistical package –Can separate exploration and analysis Can appear more “black-box” to students –Coding vs. specifying values Set-up Cost

37. Implementation Suggestions Consider learning curve of students and course goals –How familiar should they be with this package –How much do you have to step them through the exploration Minimize distractions –Consistency –Preserve contextual link

38. Implementation Suggestions Carefully design activities to achieve learning goals (the hard part!) –Guide student interaction –Always start with tactile simulations –Ease students to natural next step –Utilize instant feedback capabilities –Require student prediction in advance

39. Implementation Suggestions Provide follow-up instruction –Allow debriefing opportunities –After student exploration –Promote constructive, collaborative learning –Simultaneously design assessments Pick and choose your spots –Address most prevalent misconceptions –Emphasize power of simulation as general problem solving tool

40. Hopes for the Future More visual, interactive, dynamic and user-friendly More user control of settings More collaboration among programmers, statisticians, users

41. Take-Home Message Technology can be effective for helping students to learn statistical concepts Standard software packages can be useful –Start with the concept you want to address and the learning activity to guide student interaction Specifically designed software can be very useful –Minimize transition time and learning curve, maximize accessibility