Facilitating Student Projects in Statistics

Teaching Strategies to Make Statistics Concepts Meaningful Georgia Mathematics Conference October 18, 2012

Dianna SpenceGregg VelatiniNorth Georgia College & State University

This work supported by grants NSF DUE-0633264 and NSF DUE-1021584

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Whats In StoreSample Learning TasksExplorationsExperiencing Statistics ConceptsProjectsSynthesizing and Applying Simulations:Establishing Reasoning behind Statistical InferenceCCGPSUnderstand and evaluate random processes underlying statistical experimentsMake inferences and justify conclusions from sample surveys, experiments, and observational studies

2Explorations: Sampling

Teacher request: Please hold questions or ask them privatelyPopulation: All words in the Gettysburg AddressTask: Obtain a representative sample from this population

GettysburgAddressRandom Numbers (TI-83/84 Family)

SuggestionsCompare student values for first random numberPress arbitrary number of times to randomize BEFORE starting sampleWhat about repeats?Same random number?Same word? Typical Student Data3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5BEFOREAFTERExplorations: Comparing DataScenariosHeightMemorizing lettersKey IdeasVariableObservation vs. ExperimentTreatmentRandom AssignmentBlind Treatment

ProjectsStudent tasksIdentify research questionsDefine suitable variables, including how to quantify and measure variables Submit project proposal and obtain approvalCollect data Design unbiased data collection methodAddress sampling issuesAnalyze and interpret dataWrite a report on methods and resultsPresent research and findings to class

7Available ResourcesStudent GuideInstructor GuideTechnology GuideAppendicesA E: for students and instructorsT1 T3: for instructors

Available online: http://faculty.northgeorgia.edu/DJSpence/NSF/materials.html

Sources of Data: 3 Categories Administer surveysStudent constructs a survey and has people fill it out

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

SurveysSEEKAVOIDEXAMPLESNeutralityBias in wordingLeading questionsHighly charged wordsShould the government waste money on unemployed bums?Do you support government spending on unemployment programs?ClarityConfusing questionsVerbose questionsPoorly worded questionsInsufficient context/structureHow many times have you assisted a classmate or friend with homework, papers, worksheets, or other school-related assignments?How many times in the last week have you helped a peer with school work?PrecisionAmbiguous questionsInsufficient answer optionsDo you avoid sugar and caffeine, or do you consume both?Do you limit sugar intake?Do you limit caffeine intake?AccuracyEstimates and guessesInformation not easily recalledOn average, how many hours a night do you sleep?How many total hours have you slept over the last 3 days?SurveysWhats wrong with these?

What religion are you? (circle one)Methodist Baptist Catholic Muslim Jewish

On a scale of 1 to 10, how stressed are you?

11SurveysA construct to measure stress

Please mark each statement that is true about you.

__If I could stop worrying so much, I could accomplish a lot more.__Currently, I have a high level of stress.__In this point in my life I often feel like I am overwhelmed.__I have a lot to do, but I just feel like I cant get ahead or even sometimes keep up.__I often worry that things wont turn out like they should.__I have so much going on right now, sometimes I just feel like I want to scream.

Score 1 for each checked box. Range is 0 to 6, with higher numbers indicating higher levels of stress.12SurveysSome considerations:Consider using scales/constructse.g., Appendices B,CMaintain confidentialityUse anonymous surveys for sensitive data

Internet Data SourcesI. Government/CommunityCensus Bureau: http://www.census.gov/ Bureau of Justice Statistics: http://bjs.ojp.usdoj.gov/index.cfm?ty=daa City Data Site: http://www.city-data.com/ State and county statistics sitesState and national Dept.s of EducationCounty tax assessment records

Internet Data SourcesII. Restaurants: Nutrition InfoApplebees Nutrition Guide Arby's Nutrition Guide Burger King Nutrition Guide IHOP Nutrition GuideKFC Nutrition Guide Longhorn Nutrition GuideMcDonald's Nutrition Guide Olive Garden Nutrition GuideRuby Tuesday's Nutrition Guide Subway Nutrition GuideTaco Bell Nutrition GuideGoogle YOUR favorite place to eat!

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

General Sports Reference Sitewww.sports-reference.com

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

Individual team sites

Internet Data SourcesIV. Retail/Consumer (General)Cost/Prices e.g., Kelley Blue Book: http://www.kbb.com/

Consumer Report ratings .http://www.consumerreports.org/cro/index.htm Product Specificationse.g., size measurements,time/speed measurements,MPG for cars

Sample Student Projects(See Appendix D)Matched Pairs t-Test:2-tailed: Ha predicting that on average, students rating of Coke and Pepsi would be different.t statistic =2.62P value= 0.0116 (2-tailed)Conclusion: Evidence that on average, students rated the two drinks differently (Coke was rated higher)

Participant Coke Pepsi#1 89#2 7 5...

Sample Student Projectst-Test for 2 independent samples:1-tailed: Ha predicting that on average fruit drinks have higher sugar content per ounce than fruit juicest statistic = -0.14P value= 0.5555Conclusion: Sample data did not support Ha. No evidence that on average,fruit drinks have more sugar than fruit juices.

Sample Student Projectst-Test for 2 independent samples:1-tailed: Ha predicting that in local state parks, oak trees have greater circumference than pine trees on averaget statistic = 4.78P value= 7.91 x 10 6Conclusion: 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 ProjectsMatched Pairs t-Test:1-tailed: Ha predicting on average, Wal-Mart prices would be lower than Target prices for identical items t statistic =.4429P value= 0.3294Conclusion: Mean price difference not significant; insufficient evidence that Wal-Mart prices are lower.Item WalMart Target64-oz. Motts Juice2.79 2.8912-oz LeSeur Peas1.19 1.08...

Sample Student ProjectsSample Student Projects

23Sample Student ProjectsSample Student ProjectsAssessmentWeight of projectsScoring rubricsAdvantages consistency, manageability, communication of expectationsSee Appendix T3Team member gradesAccountability of individual members

SimulationsActivities courtesy of materials by Rossman & Chance; see Rossman, Introducing Concepts of Statistical Inference

Scenario #1:Babies reactions to mean and nice toyshttp://statweb.calpoly.edu/bchance/applets/BinomDist3/BinomDist.html

SimulationsActivities courtesy of materials by Rossman & Chance; see Rossman, Introducing Concepts of Statistical Inference

Scenario #2:Dolphin therapy for depressionhttp://www.rossmanchance.com/applets/Dolphins/Dolphins.html

Discussion / Q&A