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Championing Statistical Thinking

Championing Statistical Thinking. An ASA INSPIRE Project Student: Sr. Alice Hess , Archbishop Ryan HS Philadelphia PA Mentor: Prof. Robert Carver Stonehill College, Easton MA. USCOTS May 20 2005 The Ohio State University, Columbus OH USA.

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Championing Statistical Thinking

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  1. Championing Statistical Thinking An ASA INSPIRE Project Student: Sr. Alice Hess, Archbishop Ryan HS Philadelphia PA Mentor: Prof. Robert Carver Stonehill College, Easton MA USCOTS May 20 2005 The Ohio State University, Columbus OH USA

  2. INSPIRE:  INsight into Statistical Practice, Instruction and REasoning • UCLA & Cal Poly, San Luis Obispo, in collaboration with the ASA, created a professional development program for high school teachers preparing to teach introductory statistics courses. • Supported by the National Science Foundation (NSF) • Designed and taught by leading statistics educators and experienced secondary teachers.

  3. INSPIRE:  INsight into Statistical Practice, Instruction and REasoning • Objectives for teachers: • Teach an introductory statistics class following the AP Statistics curriculum • Learn & understand concepts and methods of introductory statistics • Use real data, active learning and technology to teach statistics • Understand statistics as a comprehensive approach to data analysis • Become familiar with a variety of resources for teaching introductory statistics • http://inspire.stat.ucla.edu/

  4. Drawing on the Olympics • Authors sought to develop AP Stats assignments that • Appeal to student interests • Use real data • Develop important concepts • Apply key techniques • Inform important conclusions • Transfer between TI-83 & Minitab platforms

  5. Populations & Variables • Participation counts & rates in summer Olympics 1900—2004 • Winning times in Men’s 100m backstroke, 1900-2000. • Men & Women’s Marathon finishing times in Summer Olympics 2004. • Qualifying Times for 800m Women’s Freestyle Swimming from Sydney and Athens Games. • Medal counts by nation, region, population of participating countries.

  6. Goals & assignments: Description

  7. Goals & assignments: Inference

  8. Describing a distribution • IDEAS to discuss: • Why does the upper distribution have 2 peaks? • Center—what does an average tell us about a distribution? • Shape—why are these skewed? • Spread—what does spread look like at the finish line? • Information in ranks (medals) vs. measurements (time)

  9. Non-linear time series Why does a curve curve? What use is a model?

  10. Comparing 2 samples • Women’s qualifying times for 800m Freestyle • Participants from Sydney (n=26) & Athens (n=29) games • Eight women competed in both games, 47 swam in one or the other. • May we treat samples as independent? • What do these samples suggest about changes in the population qualifying times?

  11. Assignment • Attached are qualifying times in the 800m women’s freestyle swimming event from the Sydney 2000 and Athens 2004 Olympic Games. • There are 55 observations in all, 26 from Sydney and 29 from Athens. • Of these swimmers, how many of the women qualified in both games? • What question does this raise? • How might this data be used to answer the question: Do female swimmers seem to be improving in general? • Do some exploratory analysis of the data first to get a “feel for” the answer to the question. Perform a test of hypothesis. Also answer the question using a confidence interval approach.

  12. Regression: units & inference Do larger countries have a predictable advantage in the Medal race? Which countries might these be?

  13. Regression Results Regression Analysis: Total2004 versus Pop2004 The regression equation is Total2004 = 10.1 + 0.000000 Pop2004 Predictor Coef SE Coef T P Constant 10.057 2.183 4.61 0.000 Pop2004 0.00000004 0.00000001 3.19 0.002 S = 17.8104 R-Sq = 12.2% R-Sq(adj) = 11.0% Analysis of Variance Source DF SS MS F P Regression 1 3223.3 3223.3 10.16 0.002 Residual Error 73 23156.4 317.2 Total 74 26379.8 Items to discuss…

  14. Comments on Pilot Results • Students rose to the challenge • Most could apply theory & technique to these tasks and datasets • Students could relate to stories in the data • Importance of a committed, skillful classroom teacher

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