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Enhancing the Teaching of Statistics with Consulting Experiences

Enhancing the Teaching of Statistics with Consulting Experiences. Christopher J. Malone Email: cmalone@winona.edu. Some initial thoughts…. Your Constraints. Your constraints A structured syllabus which must be approved by College Board Getting students to pass the AP Exam.

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Enhancing the Teaching of Statistics with Consulting Experiences

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  1. Enhancing the Teaching of Statistics with Consulting Experiences Christopher J. Malone Email: cmalone@winona.edu

  2. Some initial thoughts… Your Constraints Your constraints A structured syllabus which must be approved by College Board Getting students to pass the AP Exam

  3. Some initial thoughts… Your Constraints My Freedoms Your constraints A structured syllabus which must be approved by College Board Getting students to pass the AP Exam My freedoms A flexible syllabus written for our Department Getting students to pass MY Exams Likely their last statistics class

  4. Sequencing Sequencing of topics

  5. Sequencing Sequencing of topics Why is it the way it is? Our roots are in mathematics and historicallymathematical concepts tend to be introduced prior to applications.

  6. Sequencing Sequencing of topics Research Question #1: Do more than 1 in 4 women need supplements? Research Question #2: Is the average Forearm T Score greater than 0?

  7. Sequencing Sequencing of topics Research Question: Do more than 1 in 4 women need supplements?

  8. Sequencing Sequencing of topics Research Question: Does the diagnosis using the Spine agree with the Forearm?

  9. Sequencing Sequencing of topics Research Question: Do the average BMI levels vary across spine diagnosis?

  10. Sequencing Sequencing of topics Research Question: Do the average BMI levels vary across spine diagnosis? 2 Groups for Spine Category: T-test 3 Groups for Spine Category: ANOVA

  11. Sequencing Sequencing of topics Research Question: Do the average BMI levels vary across spine diagnosis? This difference is ‘small’ from a client’s (or student’s) perspective, but ‘huge’ to us. 2 Groups for Spine Category: T-test 3 Groups for Spine Category: ANOVA

  12. Sequencing Sequencing of topics Research Question: What is the relationship between Spine and Forearm T Scores?

  13. Sequencing Sequencing of topics

  14. Sequencing Sequencing of topics Why change?

  15. Sequencing Sequencing of topics Why change? Students carry out a complete statistical analysis over-and-over, several times through-out the course Give students exactly what they need, in the exact amount, at precisely the right time

  16. Sequencing Sequencing of topics Why change? Students carry out a complete statistical analysis over-and-over, several times through-out the course Give students exactly what they need, in the exact amount, at precisely the right time Mimics how we do analyses for consulting clients Mimics how we do analyses for consulting clients

  17. Thinking Statistical Thinking Too much ___________ hinders statistical thinking

  18. Thinking Statistical Thinking Language Too much ___________ hinders statistical thinking

  19. Thinking Statistical Thinking Language Too much ___________ hinders statistical thinking

  20. Thinking Statistical Thinking Procedure Too much ___________ hinders statistical thinking

  21. Thinking Statistical Thinking Procedure Too much ___________ hinders statistical thinking

  22. Thinking Statistical Thinking Procedure Notes from my PAST Too much ___________ hinders statistical thinking

  23. Thinking Statistical Thinking Structure Too much ___________ hinders statistical thinking

  24. Thinking Statistical Thinking Structure Too much ___________ hinders statistical thinking An exam question from my PAST

  25. Thinking Statistical Thinking Structure Too much ___________ hinders statistical thinking Client’s Interest

  26. Example 1 Example #1: Bone Density Data Question Can Forearm bone density be used as a substitute for bone density via the Spine?

  27. Example 1 Example #1: Bone Density Data Question Can Forearm bone density be used as a substitute for bone density via the Spine? Response: T Scores Variable of Interest: T Scores

  28. Example 1 Bone Density Data Question Can Forearm bone density be used as a substitute for bone density via the Spine? This is it?

  29. Example 1 Bone Density Data Question Can Forearm bone density be used as a substitute for bone density via the Spine? This is it? Well, no…

  30. Example 1 Bone Density  The Data 

  31. Example 1 Bone Density What does a client use to make decisions? Intuition

  32. Example 1 Bone Density What does a client use to make decisions? Intuition Experience

  33. Example 1 Bone Density What does a client use to make decisions? Intuition Experience Statistician

  34. Example 1 Bone Density What does a client use to make decisions? Intuition Experience Statistician (only as a last resort)

  35. Example 1 When intuition goes awry

  36. Example 1 or person-to-person comparisons Data Getting ‘new’ data . . .

  37. Example 1 Getting ‘new’ data Data The ‘new’ Data

  38. Example 1 Finally, a p-value Data Analysis

  39. Example 1 Finally, a p-value Data Analysis Conclusion We have enough statistical evidence, using a 5% error rate, to suggest that the average difference is different than zero (p-value = 0.0371).

  40. Example 1 95% Confidence Interval Conclusion We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. 95% CI

  41. Example 1 95% Confidence Interval Conclusion We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. 95% CI Client: I am sorry, but I don’t understand

  42. Example 1 95% Confidence Interval Conclusion We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. 95% CI Client: I am sorry, but I don’t understand Me:We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50.

  43. Example 1 95% Confidence Interval Conclusion We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. 95% CI Client: I am sorry, but I don’t understand Me:We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. Client: I heard you, I just don’t get it Me: We are certain that, on average, the Forearm T Score will be about ½ unit higher than the Spine T Score.

  44. Example 1 95% Confidence Interval Conclusion 95% CI ::Client: I heard you, I just don’t get it Me: We are certain that, on average, the Forearm T Score will be about ½ unit higher than the Spine T Score. Client:Great, I understand now. Are we ½ unit off on the lower end – the osteopenia / osteoporosis end? Me: I have no idea, but on average the difference… Client:I’m sorry – I need to get going now…

  45. Example 1 95% Confidence Interval Conclusion We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. 95% CI Client: I am sorry, but I don’t understand Me:We are 95% certain that the average difference between Forearm and Spine for the population is between 0 and 0.50. Client: I heard you, I just don’t get it Me: We are certain that, on average, the Forearm T Score will be about ½ unit higher than the Spine T Score.

  46. Example 1 My client left thinking I ignored the actual data In some sense, she was right!

  47. Example 1 Bringing the data back

  48. Example 1 Bringing the data back

  49. Example 1 Patience is a virtue

  50. Example 1 Patience is a virtue

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