Championing Statistical ThinkingAn ASA INSPIRE Project

Student: Sr. Alice Hess, Archbishop Ryan HS

Philadelphia PA

Mentor: Prof. Robert Carver Stonehill College, Easton MA

USCOTS May 20 2005The Ohio State University, Columbus OH USA

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.

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/

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

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.

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

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?

TimeMin

Gender

224210196182168154140

F

M

2004 Marathon Finish TimesMen separated from Women

TimeMin224210196182168154140

2004 Marathon Finish Times

Men & Women combined

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)

Non-linear time series

Year

Seco

nds

2000199219841976196819561948193219241912

85

80

75

70

65

60

55

50

Winning Time Mens' 100m Backstroke1908-2000

WhyWhy does a curve does a curve curve?curve?

What use is a model?What use is a model?

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?

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.

Regression: units & inference

Pop2004

Tota

l2004

1400000000120000000010000000008000000006000000004000000002000000000

100

80

60

40

20

0

Scatterplot of Total2004 vs Pop2004

Do larger countries have a predictable advantage in the Medal race?

Which countries might these be?Which countries might these be?

Regression ResultsRegression Analysis: Total2004 versus Pop2004

The regression equation isTotal2004 = 10.1 + 0.000000 Pop2004

Predictor Coef SE Coef T PConstant 10.057 2.183 4.61 0.000Pop2004 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 PRegression 1 3223.3 3223.3 10.16 0.002Residual Error 73 23156.4 317.2Total 74 26379.8

Items to discuss…Items to discuss…

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