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