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Teaching Statistical Concepts with Activities, Data, and Technology

Teaching Statistical Concepts with Activities, Data, and Technology. Beth L. Chance and Allan J. Rossman Dept of Statistics, Cal Poly – San Luis Obispo. Goals. Acquaint you with recent recommendations and ideas for teaching introductory statistics Including some very “modern” approaches

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Teaching Statistical Concepts with Activities, Data, and Technology

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  1. Teaching Statistical Concepts with Activities, Data, and Technology Beth L. Chance and Allan J. Rossman Dept of Statistics, Cal Poly – San Luis Obispo

  2. Goals • Acquaint you with recent recommendations and ideas for teaching introductory statistics • Including some very “modern” approaches • On top of some issues we consider essential • Provide specific examples and activities that you might plug into your courses • Point you toward online and print resources that might be helpful

  3. Schedule • Introductions • Opening Activity • Activity Sessions • Data Collection • Data Analysis << lunch>> • Randomness • Statistical Inference • Resources and Assessment • Q&A, Wrap-Up

  4. Requests • Participate in activities • 23 of them! • We’ll skip/highlight some • Play role of student • Good student, not disruptive student! • Feel free to interject comments, questions

  5. GAISE • Emphasize statistical literacy and develop statistical thinking • Use real data • Stress conceptual understanding rather than mere knowledge of procedures • Foster active learning in the classroom • Use technology for developing conceptual understanding and analyzing data • Use assessments to improve and evaluate student learning www.amstat.org/education/gaise

  6. Opening Activity • Naughty or nice? (Nature, 2007) • Videos: http://www.yale.edu/infantlab/socialevaluation/Helper-Hinderer.html • Flip 16 coins, one for each infant, to decide which toy you want to play with (heads=helper) • Coin Tossing Applet: http://www.rossmanchance.com/applets

  7. 3S Strategy • Statistic • Simulate • “Could have been” distribution of data for each repetition (under null model) • “What if” distribution of statistics across repetitions (under null model) • Strength of evidence • Reject vs. plausible

  8. Summary • Use real data/scientific studies • Emphasize the process of statistical investigation • Stress conceptual understanding • Idea of p-value on day 1/in one day! • Foster active learning • You are a dot on the board • Use technology • Could this have happened “by chance alone”? • What if only 10 infants had picked the helper?

  9. Data Collection Activities: Activity 2: Sampling Words • Circle 10 representative words in the passage • Record the number of letters in each word • Calculate the mean number of letters in your sample • Dotplot of results…

  10. Sampling Words • The population mean of all 268 words is 4.295 letters • How many sample means were too high? • Why do you think so many sample means are too high?

  11. Sampling Words • “Tactile” simulation • Ask students to use computer or random number table to take simple random samples • Determine the sample mean in each sample • Compare the distributions

  12. Sampling Words • Java applet • www.rossmanchance.com/applets/ • Select “Sampling words” applet • Select individual sample of 5 words • Repeat • Select 98 more samples of size 5 • Explore the effect of sample size • Explore the effect of population size

  13. Morals: Selecting a Sample • Random Sampling eliminates human selection bias so the sample will be fair and unbiased/representative of the population. • While increasing the sample size improves precision, this does not decrease bias.

  14. Activity 3: Night Lights and Near-Sightedness • Quinn, Shin, Maguire, and Stone (1999) • 479 children • Did your child use a night light (or room light or neither) before age 2? • Eyesight: Hyperopia (far-sighted), emmetropia (normal) or myopia (near-sighted)?

  15. Night Lights and Near-Sightedness

  16. Night Lights and Near-Sightedness

  17. Morals: Confounding • Students can tell you that association is not the same as causation! • Need practice clearly describing how confounding variable • Is linked to both explanatory and response variables • Provides an alternative explanation for observed association

  18. Activity 4: Have a Nice Trip • Can instruction in a recovery strategy improve an older person’s ability to recover from a loss of balance? • 12 subjects have agreed to participate in the study • Assign 6 people to use the lowering strategy and 6 people to use the elevating strategy • What does “random assignment” gain you?

  19. Have a Nice Trip • Randomizing subjects applet • How do the two groups compare?

  20. Morals • Goal of random assignment is to be willing to consider the treatment groups equivalent prior to the imposition of the treatment(s). • This allows us to eliminate all potential confounding variables as a plausible explanation for any significant differences in the response variable after the treatments are imposed.

  21. Activity 5: Cursive Writing • Does using cursive writing cause students to score better on the SAT essay?

  22. Morals: Scope of Conclusions The Statistical Sleuth, Ramsey and Schafer

  23. Activity 6: Memorizing Letters • You will be asked to memorize as many letters as you can in 20 seconds, in order, from a sequence of 30 letters • Variables? • Type of study? • Comparison? • Random assignment? • Blindness? • Random sampling? • More to come …

  24. Morals: Data Collection • Quick, simple experimental data collection • Highlighting critical aspects of effective study design • Can return to the data several times in the course

  25. Data Analysis ActivitiesActivity 7: Matching Variables to Graphs • Which dotplot belongs to which variable? • Justify your answer

  26. Morals: Graph-sense • Learn to justify opinions • Consistency, completeness • Appreciate variability • Be able to find and explain patterns in the data

  27. Activity 8: Rower Weights • 2008 Men’s Olympic Rowing Team

  28. Rower Weights Mean Median Full Data Set 197.96 205.00 Without Coxswain 201.17 207.00 Without Coxswain or 209.65 209.00 lightweight rowers With heaviest at 249 210.65 209.00 With heaviest at 429 219.70 209.00 Resistance....

  29. Morals: Rower Weights • Think about the context “Data are numbers with a context” -Moore • Know what your numerical summary is measuring • Investigate causes for unusual observations • Anticipate shape

  30. Activity 9: Cancer Pamphlets • Researchers in Philadelphia investigated whether pamphlets containing information for cancer patients are written at a level that the cancer patients can comprehend

  31. Cancer Pamphlets

  32. Morals: Importance of Graphs • Look at the data • Think about the question • Numerical summaries don’t tell the whole story • “median isn’t the message” - Gould

  33. Activity 10: Draft Lottery • Draft numbers (1-366) were assigned to birthdates in the 1970 draft lottery • Find your draft number • Any 225s?

  34. Draft Lottery

  35. month median January 211.0 February 210.0 March 256.0 April 225.0 May 226.0 June 207.5 month median July 188.0 August 145.0 September 168.0 October 201.0 November 131.5 December 100.0 Draft Lottery

  36. Draft Lottery

  37. Morals: Statistics matters! • Summaries can illuminate • Randomization can be difficult

  38. Activity 11:Televisions and Life Expectancy • Is there an association between the two variables? • So sending televisions to countries with lower life expectancies would cause their inhabitants to live longer? r = .743

  39. Morals: Confounding • Don’t jump to conclusions from observational studies • The association is real but consider carefully the interpretation of graph and wording of conclusions (and headlines)

  40. Activity 6 Revisited (Memorizing Letters) • Produce, interpret graphical displays to compare performance of two groups • Does research hypothesis appear to be supported? • Any unusual features in distributions?

  41. Lunch! • Questions? • Write down and submit any questions you have thus far on the statistical or pedagogical content…

  42. Exploring RandomnessActivity 12: Random Babies Last Names First Names Jones Jerry Miller Marvin Smith Sam Williams Willy

  43. Random Babies Last Names First Names Jones Marvin Miller Smith Williams

  44. Random Babies Last Names First Names Jones Marvin Miller Willy Smith Williams

  45. Random Babies Last Names First Names Jones Marvin Miller Willy Smith Sam Williams

  46. Random Babies Last Names First Names Jones Marvin Miller Willy Smith Sam Williams Jerry

  47. Random Babies Last Names First Names Jones Marvin Miller Willy Smith Sam 1 match Williams Jerry

  48. Random Babies • Long-run relative frequency • Applet: www.rossmanchance.com/applets/ • “Random Babies”

  49. Random Babies: Mathematical Analysis 1234 1243 1324 1342 1423 1432 2134 2143 2314 2341 2413 2431 3124 3142 3214 3241 3412 3421 4123 4132 4213 4231 4312 4321

  50. Random Babies 1234 1243 1324 1342 1423 1432 4 2 2 1 1 2 2134 2143 2314 2341 2413 2431 2 0 1 0 0 1 3124 3142 3214 3241 3412 3421 1 0 2 1 0 0 4123 4132 4213 4231 4312 4321 0 1 1 2 0 0

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