Student Projectsin Statistics

GCTM ConferenceOctober 14, 2010

Dianna Spence

NGCSU Math/CS Dept, Dahlonega, GA

Background: NSF Grants• The material shared in this presentation is the

product of work supported by 2 NSF Grants.

• Phase I Grant (2007-2010) “Authentic, Career-Specific Discovery Learning Projects in Introductory Statistics” Developed and pilot tested curriculum materials

to facilitate discovery projects in statistics Measured 3 specific student outcomes

• Phase II Grant (2010-2014)“Discovery Learning Projects in Introductory Statistics” Refine & improve materials Pilot test nationally Improve assessment of outcomes

Website Resources

http://radar.northgeorgia.edu/~djspence

What’s on this website?

• This presentation

• NSF Main Project Information Page

• Phase I Instructional Materials (OLD)

• Phase II Instructional Materials These will be posted as they are

developed over the next year

Types of Projects• Linear regression*

• Chi-squared tests

*Part of NSF supported work

• t-tests* Designs

• 1-Sample• 2 Independent

samples• 2 Dependent

samples

Project Tasks for Students• Identifying research questions

• Defining specific variables

• Data collection Finding sources of data

• Designing surveys if applicable Identifying & implementing a sampling strategy

• Organizing and recording data

• Appropriate analysis of data

• Interpretation of results

• Reporting results (written and oral)

Today’s Focal Points

• Where can students get authentic data?

• What kinds of research questions do students investigate?

• How are student outcomes measured? Evaluation of student work Assessing the benefit of projects/materials Improving our instruments and findings

Collecting Data: 3 Categories

• Administer surveys Primary focus of Phase I materials Makes survey design an element of the project

• Find data on the Internet

• Physically go out and record datae.g., measure items, time eventswith a stopwatch, look at prices, look at nutrition labels

Internet Data SourcesI. Government/Community• Census Bureau: http://www.census.gov/

• Georgia Statistics System: http://www.georgiastats.uga.edu/

• City Data Site: http://www.city-data.com/

• Bureau of Justice Statistics: http://bjs.ojp.usdoj.gov/index.cfm?ty=daa

• Georgia Dep’t. of Education reporting page: http://www.doe.k12.ga.us/datareporting.aspx

• Georgia Tax Assessors: http://gaassessors.com/

Internet Data SourcesII. Restaurants: Nutrition Info

• Applebees: http://www.applebees.com/downloads/nutritional_info.html

• Arby’s: http://www.arbys.com/nutrition/Arbys_Nutrition_Website.pdf

• Burger King: http://www.bk.com/cms/en/us/cms_out/digital_assets/files/pages/NutritionInformation.pdf

• McDonalds: http://nutrition.mcdonalds.com/nutritionexchange/nutritionfacts.pdf

• Ruby Tuesday’s: http://www.rubytuesday.com/assets/menu/pdf/informational/nutrition.pdf

• Student’s favorite place to eat?

Internet Data SourcesIII. Sports Data

• Sports Statistics Data Resources (Gateway) http://www.amstat.org/sections/SIS/Sports Data Resources/

• NFL Historical Stats: http://www.nfl.com/history

• Individual team sites

Internet Data SourcesIV. Retail/Consumer (General)• Cost/Prices

• Consumer Report ratings .http://www.consumerreports.org/cro/index.htm

• Product Specifications e.g., size measurements,

time/speed measurements,MPG for cars

Sample Student Projects

• One Sample t-Test: 1-tailed:

Ha predicting that the average purebred Boston Terrier puppy in the U.S. costs more than $500

Stratified sample representing different regions of the country

t statistic =1.73 P value= 0.0449 Conclusion: Evidence at

0.05 significance level that on average, purebred Boston Terrier puppies are priced higher than$500.00 in the U.S.

Sample Student Projects

• Matched Pairs t-Test: 1-tailed: Ha predicting on average, Wal-Mart prices

would be lower than Target prices for identical items t statistic =.4429 P value= 0.3294 Conclusion: Mean price difference not significant;

insufficient evidence that Wal-Mart prices are lower

Item WalMart Target

64-oz. Mott’s Juice 2.79 2.89

12-oz LeSeur Peas 1.19 1.08

.

.

.

Sample Student Projects

• Matched Pairs t-Test: 2-tailed: Ha predicting that on average, students’

rating of Coke and Pepsi would be different. t statistic =2.62 P value= 0.0116 (2-tailed) Conclusion: Evidence that on average, students rated

the two drinks differently (Coke was rated higher)

Participant Coke Pepsi

#1 8 9

#2 7 5

.

.

.

Sample Student Projects

• t-Test for 2 independent samples: 1-tailed: Ha predicting that on average fruit drinks

have higher sugar content per ounce than fruit juices t statistic = -0.14 P value= 0.5555 Conclusion: Sample data did not support Ha.

No evidence that on average,fruit drinks have more sugar than fruit juices.

Sample Student Projects

• t-Test for 2 independent samples: 1-tailed: Ha predicting that in local state parks, oak

trees have greater circumference than pine trees on average

t statistic = 4.78 P value= 7.91 x 10 –6

Conclusion: Strong evidence that in local state parks oak trees are bigger than pine trees on average.

Lurking variable identifiedand discussed: age of trees (and possible reasons that oak trees were older)

Sample Student Projects

0 50 100 150 200 250 300 350 400 4500

5

10

15

20

25

f(x) = 0.0478332095327044 x − 0.428366385027227R² = 0.562802131100638

Snack Food Fat Content and Calories

Calories Per Serving

Fat

Co

nte

nt

(gra

ms)

per

ser

vin

g

Sample Student Projects

10 15 20 25 30 35 40 45 50 55 600

5

10

15

20

25

30

35

40

45

50

f(x) = − 0.660605999759046 x + 36.7883619131762R² = 0.277004149772465

Age and Binge Drinking (Survey Score)

Ages

Sco

re f

rom

Su

rvey

Sample Student Projects

0 100 200 300 400 500 6000

10

20

30

40

50

60

f(x) = − 0.0396724503190436 x + 34.6940040072173R² = 0.605113434464562

Engine Horsepower andAverage MPGs

Engine Horsepower

Ave

rag

e M

PG

s

Sample Student Projects

Sample Student Projects

12 17 22 27 32 37 42

40

50

60

70

80

90

100

f(x) = 0.0950938851700572 x + 74.717428620174

Correlation & Regression: QB Ratings and Wonderlic Score

Wonderlic Score

Car

eer

QB

Rat

ing

Sample Student Projects

0 5 10 15 20 250.170.190.210.230.250.270.290.310.33

f(x) = 0.000120323014804848 x + 0.256368470165994R² = 0.000260932869447394

Batting Averages vs. Years in the MLB

Years in the MLB

Bat

tin

g A

vera

ge

Online Resource:Materials for Students (OLD)

• Student GuideOverall Project Guide

• Help for each project phaseTechnology GuideVariables and Constructs

Online Resource:Instructional Materials (OLD)

• Instructor GuideProject overview

• Timelines• Implementation tips• Best practices

Handouts for different project phases

Evaluation rubricsLinks to student resources

Assessment

• Scoring RubricsAdvantages

• Consistency• Manageability• Communicate expectations

Encompass All Project Components• Grade milestones along the way

Resources for Rubrics

Phase I Assessment of Outcomes • Varied by Instructor• Overall results given here• Instrument

Perceived Usefulness• Pretest: 50.42• Posttest: 51.40• Significance: p = 0.208

Self-Beliefs for Statistics• Pretest: 59.64• Posttest: 62.57• Significance: p = 0.032**

Content Knowledge• Pretest: 6.78• Posttest: 7.21• Significance: p = 0.088*

Multivariate Analysis: Content Knowledge

Multivariate Analysis: Statistics Self-Efficacy

Qualitative Findings:Student FeedbackStudent Quotes Shared by Instructors

“The main thing that we have learned is that statistics take time. They cannot be conjured up by a few formulas in a few minutes. The

time and effort that is put into a small research project such as this is significant.

On a large scale, one can quickly understand the kind of commitment of money and time that is required just to obtain reasonable

data.”

“While our results did not meet our initial expectations, this is not an utter disappointment. Before this project, statistics looked simple enough for anyone to sit down

and do, but now it is evident that it requires more creativity and critical thinking than initially expected. Overall, it was

an edifying experience.”

Improving Our Assessments• Perceived Usefulness

Reduce/eliminate focus on career

• Content Knowledge Add questions to reflect what student knows

about conducting research• Data collection methods• Sampling strategies• Organizing and analyzing data

Website Resources

http://radar.northgeorgia.edu/~djspence

What’s on this website?

• This presentation

• NSF Main Project Information Page

• Phase I Instructional Materials (OLD)

• Phase II Instructional Materials These will be posted as they are

developed over the next year