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Teaching Statistics

Teaching Statistics. Marty Triola mftriola@aol.com. Insider’s Guide to Teaching with the Triola Statistics Series. For adjuncts and full-time profs: How to teach statistics Comments, objectives, activities Choosing a technology General teaching tips Syllabi, supplements, extra data sets.

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Teaching Statistics

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  1. Teaching Statistics Marty Triola mftriola@aol.com

  2. Insider’s Guide to Teaching with the Triola Statistics Series For adjuncts and full-time profs: • How to teach statistics • Comments, objectives, activities • Choosing a technology • General teaching tips • Syllabi, supplements, extra data sets

  3. ASA: GAISE Recommendations • Statistical literacy and statistical thinking • Use real data • Understanding rather than procedures • Foster active learning • Use technology • Use assessments

  4. In addition to teaching statistics, we can help our students grow through developing …

  5. Important Life Skills • Critical thinking • Technology • Collaboration • Speaking

  6. Implementing GAISE • Beyond formulas, much interpretation • Project!!!!!!!!!! • Real data • Technology for technology • Technology for new topics • Technology for different methods: Simulation, bootstrap

  7. Beyond Formulas Find P(20 girls in 20 births). Is 20 girls in 20 births… unusual? Why?

  8. Beyond Formulas Data from Atkins weight loss program: n = 40, mean loss = 4.6 lb, SD = 10.6 lb. Test the claim that the diet has no effect. Would you recommend it? Why or why not?

  9. Beyond Formulas Teaching standard deviation …

  10. Single bank line: 4, 7, 7 →→→ ■ ■ ■ Multiple lines: 1, 3, 14 ↓ ↓ ↓ ■ ■ ■

  11. Project!!!

  12. Give someone a fish and you have fed them for today. Teach someone to fish and you have fed them for a lifetime.

  13. Tell me something and I’ll forget. Show me and I’ll remember. Involve me and I’ll learn.

  14. Touch Therapy • Emily Rosa: 9 yrs old • 280 trials: 44% correct • JAMA

  15. Survey • ___Female ___Male • Eye color: __________ • Enter five random digits:__ __ __ __ __ • Enter height in inches: __________ • Enter last 5 digits of SSN: __ __ __ __ __ • Record pulse rate for 1 min.: ______ • Do you smoke? _____ • Do you exercise? _____

  16. George Cobb article about evaluating introductory statistics textbooks ("Introductory Textbooks: A Framework for evaluation", Journal of the American Statistical Association, Vol. 82, No. 397): “Are the Data Sets Real or Fake? . . . I hope that soon we will have seen the last of the infamous XYZ Corporation and Hospitals A, B, C, . . ."

  17. Data Types • Fabricated: Bank Lines • Simulated • Real: GOLD STANDARD

  18. With REAL data, students see . . . • some purpose in what they are doing. • examples from fields they might be pursuing. • that statistics is more than an abstract mental exercise. Statistics is used in the real world.

  19. Really Bad Exercise Give the formula for st. dev. and use it to find the st. dev. of the following sample data, and show all work: 16 5 2 0 8 8

  20. Worse Exercise The following are mean teacher salaries (in thousands) in a sample of states. Find the mean, median, and standard deviation: 37 42 55 29 41

  21. Good Exercise Use these weights (g) of new quarters. 5.71 5.71 5.59 5.61 5.63 (a) Find mean (b) Find st. dev. (c) Is a weight of 5.23 g unusual? Explain. (d) What’s wrong with minting quarters with weights that vary too much?

  22. Interesting Data • Speeding tickets: 57 42 45 . . . • Body temperatures: 98.6 • Benford's Law: USA Today

  23. 1st Digit Frequency % 1 30.1 2 17.6 3 12.5 4 9.7 5 7.9 6 6.7 7 5.8 8 5.1 9 4.6

  24. Project Do the leading digits of street addresses fit the distribution of Benford’s Law?

  25. Project: Toss Coin 200 Times Actually toss a coin or Make up the results.

  26. 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0

  27. Project Hint If you don’t do projects now, start with a small step of doing just one project.

  28. Assign near beginning of course: • Collect a set of real data. • Print computer display of desc. Stat’s. • Write a paragraph: -Describe the data. Anything unusual? -How did you collect the data? -How is the sampling method flawed?

  29. Technology • Any Scientific Calculator • TI-83/84 Plus • Minitab • STATDISK • Excel

  30. Example  • Test H0:  =98.6o • Sample Data: • n = 106, ¯ = 98.20, s = 0.62 x

  31. TI83/84 Plus: • Uses raw data or statistics • Has "APPS" capability • PValue = 0.00000000140

  32. TI-83/84 Plus Hint • Use CtlgHelp • Example: 2:normalcdf( + (press + before pressing [ENTER])

  33. TI-83/84 Plus Programs Download from www.aw.com/triola (by Michael Lloyd from Henderson State U.) Sample: • CDISTR (cumulative distributions) • TVAL (P-value for t distribution) • ANOVA2RB (2-way ANOVA) • S2TEST (hyp. test for variance) • X2GOF (Chi-sq. gooodness-of-fit) • KWTEST (Kruskal-Wallis test)

  34. NOW ALLOWS SUMMARY STATISTICS Can be bundled with textbook (or $29/5 months) Windows only: 98, ME, NT 4, 2000, XP Minitab 16 has new “Assistant” feature PValue = 0.000 One-Sample T Test of mu = 98.6 vs not = 98.6 N Mean StDev SE Mean 95% CI T P 106 98.2000 0.6200 0.0602 (98.0806, 98.3194) -6.64 0.000 Minitab:

  35. Free Very easy to use Uses raw data or statistics. PValue = 0.0000 STATDISK

  36. Excel: • Uses raw data only • PValue = 1 • Errors

  37. Excel: Add-in or STATDISK • PValue < .0001 from XLSTAT

  38. SPSS • Uses raw data only. • Has student version. • No confidence interval for p. • Hypothesis test: P-value is always two-tailed. • Must avoid conflict with field width and # decimals.

  39. SPSS (continued)

  40. Summary of PValues • TI83/84 0.00000000140 • Minitab 0.000 • STATDISK 0.0000 • Excel 1 (whoops!) • SPSS 0.000 • SAS Doesn’t work.

  41. Statistics Online • MyStatLab • MathXL

  42. Technology as a TimeSaver • After covering CI and HT for one population, use technology and assign exercises with two samples.

  43. Project Calculation: 8×7×6 ×5 ×4 ×3 ×2 ×1 or 1 ×2 ×3 ×4 ×5 ×6 ×7 ×8 Do NOT actually compute the result. Estimate the result in less than 5 seconds, then write it down.

  44. Project: Hypothesis Test Test  =98.6o • P-value • Traditional (critical value) • Confidence Interval • Simulation

  45. Simulation Hypothesis test of μ= 98.6: Sample Data: n = 106 Sample mean = 98.20 s = 0.62 Generate samples with assumed mean of 98.6 and n = 106 and s = 0.62 to know if 98.20 is likely to occur by chance.

  46. Time Management Should we omit some topics to make time for projects and technology?

  47. YES!!! (Within Reason) “Don’t take life too seriously. You’ll never get out of it alive.”

  48. Summary • Use REAL DATA. • Do a major PROJECT. • Use technology to save time. • Go “BEYOND THE FORMULA.” Continued…

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