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. Technique, Topic, or Concept Dataset & assignment Describing a distribution (center, shape, spread) Marathon times (Men & Women’s) Olympics 2004: Descriptive statistics—showing symmetry, skewness, single- and multiple peaks. Non-linear decay in time series 100m Men’s Backstroke Swimming Event Data transformation (logs, quadratics, etc) Participation in Summer Olympics 1900-2004: Impacts of changes to encourage female participation Goals & assignments: Description

7. Goals & assignments: Inference Technique, Topic, or Concept Dataset & assignment 2-sample Confidence intervals & significance tests; independence Are swimmers getting faster? Qualifying Times—800 m Woman’s Freestyle Event from Sydney & Athens Games. Simple linear regression, including inference for slope Do large countries win more medals than smaller countries? Simple regression for 2004 summer Olympics; X = population of country, Y = # medals won. Chi-square test of Goodness of Fit Participation in Olympics 1900 to 2004 Chi-square Independence test Is medal-winning related to Olympic region?

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