section 2: data collection, sampling, and …section 2: data collection, sampling, and experimental...

Section2:DataCollection,Sampling,andExperimentalDesignThefollowingmapsthevideosinthissectiontotheTexasEssentialKnowledgeandSkillsforMathematicsTAC§111.47(c).2.01SampleSurveys

• Statistics(1)(A)• Statistics(2)(B)• Statistics(2)(C)• Statistics(2)(E)

2.02Sourcesofbiasinsamplingandsurveys

• Statistics(2)(A)• Statistics(2)(C)

2.03SamplingMethods–Part1

• Statistics(1)(A)• Statistics(2)(A)


• Statistics(1)(A)• Statistics(2)(A)• Statistics(2)(G)

2.05ExperimentsvsObservationalStudies

• Statistics(2)(B)2.06ThreePrinciplesofExperimentalDesign

• Statistics(1)(B)• Statistics(2)(C)• Statistics(2)(E)• Statistics(2)(F)

2.07LurkingandConfoundingVariables

• Statistics(2)(G)

Copyright 2017 Licensed and Authorized for Use Only by Texas Education Agency 1

2.08ConfidenceIntervalsintheRealWorld

• Statistics(1)(B)• Statistics(2)(C)• Statistics(2)(E)• Statistics(2)(F)• Statistics(2)(G)

Note:Unlessstatedotherwise,anysampledataisfictitiousandusedsolelyforthepurposeofinstruction.


2.01SampleSurveys

Samplesurvey–Designedtogatherinformationaboutasmallgroupfromapopulationofinterest

• Asampleofsubjectsistakenfromthe______________andaskedquestions.• Thesample________matters,notthepopulationsize.The_______________our

sample,themorepreciseourestimateswillbe.• Toreducebiasinsurveys,itisbesttohave__________samples.• ___________________samplesaremadeupofpeopleorsubjectsthatareeasyto

obtain.

Thedesignofasurveycanhaveamajorimpactonresults.Apoorlydesignedandimplementedstudymaybemeaninglessormisleading.

1. SupposeDr.Malcolmisresearchingthesideeffectsofadrugintendedtorelievepain.She

surveys15ofherpatientsandfindsthat40%ofthemexperiencedfatigueormuscleache.Twootherdoctorsresearchingthesamedrugfoundthatfromarandomsampleof760patientsacrossthecountry,30%experiencedfatigueormuscleache.Whichstudyismorecredible?Justifyyouranswer.


Whendesigningasurvey,thefollowingquestionsshouldbeconsidered:

• Whatarethegoals?• Whatisthetargetedpopulation?• Whatquestionswillbeasked?• Howwilltheparticipantsbeselected?• Howwillthedatabeanalyzedandpresented?

Otherquestionsmayneedtobeconsideredaswell,dependingonthecircumstances.

2. Belowarethreehypotheticalsurveyquestionsandstatements.Foreach,identifyanyflaw(s)andsuggestawaytoimproveit.

i. “Howsatisfiedareyouwithyourpay,healthbenefits,andworkload?”

ii. “WiththeincreaseinspeedingticketsonI-10thesepastfewmonths,doyouthinkthespeedlimitshouldbeincreasedsinceitseemseveryoneisdrivingfastanyway?”

iii. “Whatisyourmaritalstatus?”


2.02SourcesofBiasinSamplingandSurveys

Supposethatyouworkforaresearchagency,andyourjobincludessurveyingvotersandpredictingwhoisgoingtowintheupcomingelection.Youcall1,000voters,askwhichcandidatetheyintendtovotefor,recordandtabulatetheanswers,andmakesomepredictions.Afteryoucollectthedata,youdiscoverthatalmosteverysurveyrespondentwasalow-incomevoterandaregisteredDemocrat.Isthereaproblemwithyourdata?

Insurveysampling,_______________isdefinedasthesystematicfavoringofcertainoutcomes.

Agoodsampleis__________________,meaningthateachpersonoriteminthesampleisequallylikelytobeselectedfromthepopulation.

Bias–Theresultsobtainedfromasampledonotaccuratelyrepresentthepopulation.

SourcesofBias

• Undercoverage–Aportionofthepopulationisexcludedorunderrepresented.

Example:Thepopulationishighschoolstudents,butoursamplecontainsonlyfreshmen.

• Nonresponsebias–Peopledonotrespondtothestudy.

Example:Onehundredpeopleareselectedfromthephonebooktobesurveyed,but40ofthemhangupbeforeresponding.

• Responsebias–Thesurveydesigninfluencestheresponses.

Examples:“Doyoureallythinkweshouldhavebandandchorusinschoolwhenwehavesomanycoresubjectstolearn?”or“Doyouonlycareaboutlooks?”

SamplingTechniquesThatCreateBias

• Voluntaryresponsesample–Therespondents______________choosetosubmittheirresponses.

• Conveniencesample–Thesampleisselectedbasedoneaseandcosttotheinterviewer.


1. Supposeyoutakeasurveyaboutschoolattendance.Thewomanconductingthesurveyremindsyouofyouraunt,soyourespond“No”whensheasksifyouhaveeverbeenlatetoclass,eventhoughyouhave.Whichofthefollowingtypesofbiasis/arepresentinyourresponse:undercoverage,nonresponsebias,orresponsebias?

2. Twopollsshowsignificantlydifferentresults.Oneasks,“Doyouthinkschoolhoursshouldbedecreased?”andtheotherasks,“Doyouthinkschoolhoursshouldbedecreasedconsideringthereisnotimeforoutsideplay?”Whichofthefollowingtypesofbiasis/arepresentinthisscenario:undercoverage,nonresponsebias,orresponsebias?

3. Supposethatapoliticianwantstoknowhowtheresidentsofhisdistrictwillreacttoabillthatraisesthefullretirementageto70.HerunsthefollowingadduringSundayNightFootball:“Letusknowwhatyouthink!Wouldyoubeinfavorofraisingtheretirementageto70,orwouldyouratherkeeptheretirementageat67,whenmanyseniorsarestillproductiveandhealthyenoughtostayworking?Giveusacallat1-800-555-1111,andgiveusyouropinion!”Identifythesourcesofbiaspresentinthisad,andjustifyyouranswer.



Supposeyouareexaminingastudyandyoufindthattheresultsarebiasedbecauseoffactorssuchasundercoverageandconveniencesampling.Youareveryinterestedinthetopicandwouldliketoreplicatethestudytoproduceresultsthatareunbiasedandrepresentthepopulation.

Ingeneral,__________________________usethelawsofprobabilityintheselectionprocessandminimizesbias.

RandomSamplingTechniques

• Simplerandomsample(SRS)–Eachsubjectinthepopulationhasanequalchanceofbeingselected.Theuseofrandomnumbergeneratorsisusefulinthisprocess.

• Stratifiedrandomsampling–Thepopulationisdividedintohomogeneousgroups,andSRSsaretakenfromeachgroup.

Example:Dividingahighschoolintofreshmen,sophomores,juniors,andseniors,andtakingasimplerandomsamplefromeachgroup

• Systematicrandomsampling–Arandomnumbergeneratorisusedtodeterminevaluesfork,andtheneverykthobservationissampled.

• Clusterrandomsampling–Thepopulationisdividedintoheterogeneousgroups,andSRSsaretakenfromeachgroup.

Example:Dividingahighschoolbasedonclassperiod,randomlyselectingseveralclassrooms,andsamplingeveryoneinthoseclassrooms

• Multistagerandomsampling–Thisapproachinvolvesacombinationoftherandomsamplingmethodslistedabove.

1. SupposeMs.Abernathyisconductingresearchonteachers’attitudestowardhomeschooling.Sheisparticularlyinterestedindescribingtheattitudesofteachersfromrural,smallurban,andlargeurbanschooldistricts.WhichsamplingprocedureshouldMs.Abernathyusetoensurehersampleisrepresentativeofthesetypesofschooldistricts?


2. SupposeyouareaqualitycontrolengineerforabottlingcompanyinLaredo,Texas,thatfocusesonsoftdrinks.Yourjobistoplanandoverseethevariousstepsthatareinvolvedinprocessingandmanufacturingeachsoftdrinkproducttomakesuretheproductsmaintainthehigheststandardsofquality.Everytimeyouwanttotestaproduct,youuserandomdigitstorandomlyselectfivecansofsodafromeachbatchof50cans.Whatsamplingmethodareyouusing?Giveanexampleoftherandomselectionofcans.

3. Youareconductingapollinthemallandwanttorandomlyselectfivepeopletointerviewfromthenext100peoplethatwalkpastyou.Ifyouusethefollowingrandomdigits,whatarethefirsttwonumbersthatwillbeaddedtoyoursample?

412411756270184057528156592499

4. Youareconductingapollinthemallandwanttorandomlyselect10peopletointerviewfromthenext200peoplethatwalkpastyou.Ifyouusethefollowingrandomdigits,whatarethefirsttwonumbersthatwillbeaddedtoyoursample?

412411756270184057528156592499



1. Whichtypeofrandomornonrandomsamplingtechniqueisbeingusedineachscenariobelow?

i. Youareaqualitycontrolengineerforanorangejuicecompany.Youusethefollowingrandomdigitstorandomlyselectfivecartonsoforangejuicefromabatchof50cartonsoforangejuice.

743788300036123412325423881261

ii. PercyWeasleyisconductinganinvestigation.Herandomlysamplesfromall

studentsatHogwartsuntilhehas25Slytherins,20Gryffindors,20Ravenclaws,and15Hufflepuffs.

iii. ApollingcompanyinNewYorkwantstodeterminewhetherregisteredvotersin

thestaterecentlyvoted“Yes”onanewamendment.Theyrandomlyselect200registeredvotersfromeverycountyinthestateandaskeachpersonwhetherheorshevoted“Yes”or“No.”


2. Theownerofabusinessparkwantstosurveytheofficesinthecomplextoestimatehertenants’overallsatisfaction.Thebusinessparkhastwobuildings,oneolderandonenewer.Eachbuildinghasthreefloorsofstandardofficespace(20officesperfloor)andonetopflooroflargeoffices,whicharedoublethesize(10largeofficesperfloor).Halfoftheofficesineachbuildingfacethetwomainroads,whiletheotherhalffacealakeandseveraltrees.Currently,75%oftheofficesareoccupied.

i. Howmanyofficesaretheretotal?

ii. Explainhowtoselectasimplerandomsampleof20offices.

iii. Explainhowtoselectastratifiedrandomsampleof20offices.

iv. Explainwhyselectingtworandomfloorswouldnotbeagoodwaytoobtainaclustersample.


2.05ExperimentsandObservationalStudies

Observationalstudy–Researchersdonottrytochangeanything;theyjustobserve.

• Retrospectivestudy–Researchersselectsubjectsanddeterminetheirpreviousconditionsorbehaviors.

• Prospectivestudy–Researchersfollowsubjectstoobservefutureoutcomes.

Example:Supposeyouarestudyingthequestion“Domusicianshavebettergrades?”Youcantakeahighschoolandlookuprecords(retrospective),oryoucantakeahighschoolandtrackthenextdecade(prospective).

Experiment–Researchersmanipulatefactorlevelstocreatetreatmentsandcompareresponses.

• Experimentalunits–Subjectsorparticipants

• Response–Whatwewanttomeasure

• Factor–Categoricalvariablewithatleasttwolevels

o Level–Thespecificvaluesofafactorthattheexperimenterchooseso Treatment–Allpossiblevaluesoftheexplanatoryvariable


1. Determinewhethereachofthefollowingresearchprojectsisanexperimentoranobservationalstudy.Ifitisanobservationalstudy,identifyitasretrospectiveorprospective.

i. AresearcherwantstoknowwhichofthreesororitieshasthehighestGPA.Sherandomlysamples10womenfromeachsororityandrecordstheirGPAs.

ii. Aresearcherwantstocomparetheeffectsofthreeheadachemedications.Sherandomlyassigns20patientssufferingfromheadachestoreceiveoneoffourpills,includingaplacebo,andmeasuresthetimeuntileachpatientnolongerfeelstheheadache.

iii. Aresearcherwantstocomparethreebrandsoftires.Herandomlyassignsatirebrandto24cars,ensuresthatthecarsaredrivenundersimilarconditions,andrecordshowlongeachcar’stireslast.

iv. Aresearcherwantstocomparethesalariesoffourcollegemajors.Herandomlysamples20recentgraduatesfromeachmajorandrecordstheirsalariesoverthenext5years.


2. Ishappinessaffectedbydietandexercise?Agroupofpeopleisinvolvedinastudytotestthis.Theyaretoldwhethertoexercisealow,moderate,orhighamounteachweekandwhethertomaintainahealthyorunhealthydiet.Inthisexperiment,identifyeachofthefollowing:

i. Experimentalunits

ii. Factor(s)

iii. Level(s)

iv. Treatment(s)

v. Responsevariable


2.06ThreePrinciplesofExperimentalDesign

Threefundamentalprinciplesthathelptomakeagoodexperiment:

• Control–Thetreatmentthecontrolgroupreceivesisaplacebo.

o Ifthesubjectsdon’tknowwhichpilltheyget,thesubjectsareblind.o Iftheresearcherdoesn’tknoweither,thestudyisdouble-blind.

• Randomization–Subjectsarechosenatrandom.

o Acompletelyrandomizedisadesigninwhichtheexperimentalunitsarerandomlyassignedtothetreatmentgroups.

o Ablockdesignmaybeusedtoplacesubjectsintosimilargroupso Amatchedpairdesignisaspecialcaseofablockdesign,usedwhenthe

experimenthasonlytwotreatments.

• Replication–Severalexperimentalunitsareassignedtoeachtreatment.Thenumberofreplicationsistypicallytheratioofthenumberofexperimentalunitstothenumberoftreatments.

1. Severalmethodsofcontrolexist:placebogroup,blinding,anddouble-blinding.Writethecorrectmethodofcontrolforeachofthefollowingsituations.

i. Thetreatmentgroupisgivenafakepillbecausepeopleoftengetbettersimplybecausetheythinktheyaretakingsomethingthatwillmakethembetter.

ii. Neithertheresearcher(s)northesubjectsknowwhoisgettingwhattreatment.Thishelpstoensurealltreatmentgroupsaretreatedasequallyaspossible.

iii. Thesubjectsdonotknowwhichtreatmenttheyaregetting.Thishelpstoensurealltreatmentgroupsaretreatedasequallyaspossible.


2. Determinewhethereachofthefollowingscenariosisacompletelyrandomizeddesign,arandomizedblockdesign,oramatchedpairsdesign.Justifyyouranswer.

i. Totestfordifferencesbetweenthreebrandsofgasoline,20compactcars,20midsizedcars,20hybridcars,and20luxurycarswillberandomlyassignedoneofthethreegasolinebrands.Allthecarswillbedrivenundersimilarconditions.Thentheirmilespergallon(mpg)willbecalculatedandcompared.

ii. Afarmerwishestostudytheeffectoftwodifferentpesticidesonhisstrawberries.Hewillrandomlyassignside-by-sideplotsoffieldtoreceiveeitherpesticideornopesticide(controlgroup).Thenhewillmeasureandcomparetheyieldofstrawberrieswithinapre-determinedperiodoftimeforeachplot.

iii. Tocomparetheabilitiesofmaleandfemalefirefighters,10maleand10femalefirefighters,matchedaccordingtotheirweights,willbeaskedtorunupfiveflightsofstairswhilecarryingthesamefirehose.Thedifferencesintimeswillbedeterminedandcompared.


2.07LurkingandConfoundingVariables

Earlierwediscussedvariablesthatinfluencetheresultsofanexperiment.Twotypesofvariablescanaffecttheresultsofastudy:______________variablesand_____________variables.

Lurkingvariable–Avariablethatisnotincorporatedintothedesignofaresearchstudy

Confoundingvariable–Avariablethatisincorporatedintothedesignofaresearchstudy

Thesetwotypesofvariableshavesimilareffects.Eachdrivesthebehavioroftwoothervariablesobservedinastudy,creatinganapparentassociationbetweenthosetwovariables.However,whentwovariablesareconfounded,theyareintertwinedinsuchawaythatfiguringoutwhichofthem(orperhapswhichcombination)isaffectinganothervariableisahugechallenge.

1. Forthefollowingscenarios,statewhethertheissueiswithlurkingvariablesorconfoundingvariables.

i. Alegislatorproposesareductionoffundingforfiredepartmentsinhisstatebecauseastudyconcludedthatthemorefirefightersinvolvedinafightingafire,theworsedamagethefirecauses.

ii. Astudentconductsresearchonthedifferenceinbodymassindex(BMI)betweeneconomicsstudentsandeducationstudents.HewasinspiredbyapreviousstudythatconcludedthateconomicsstudentshavehigherBMIsthaneducationstudents.Thestudent’sadvisorsuggeststhatheincludebiologicalsexinhisstudy.Thestudentfindsthatthereisnodifferencebetweeneconomicsandeducationstudents’BMIs,challengingpreviousfindings.


2.08GeneralizationofResultsandConclusions

Whatresultscanbedrawnfromobservationalstudies,experiments,andsurveys?

________________referstotheextenttowhichthefindingsfromastudycanbegeneralized,orapplied,toalargerpopulation.Itrequires______________selection.

1. Whichofthefollowingdescribeswhenitisappropriatetogeneralizestudyresultstoalargerpopulation?

A. Inexperimentalstudies,whenparticipantsareconvenientlyselectedfromalargepopulation

B. Inexperimentalstudies,whenparticipantsarerandomlyselectedfromalargepopulation

C. Inobservationalstudies,whenparticipantsareselectedfromapoolofinterestedpeople

2. AstudyevaluatestheefficacyofaspecifictreatmentinelderlyCaucasianmenwhohavecoronaryheartdisease.

i. Discusswhencanwegeneralizeorapplytheresultsofthisstudytoalargerpopulation.

ii. SupposethatahealthcenterinyourcitywantstoapplytheresultsofthisstudytodevelopoutreachprogramsandservicesforHispanicwomenandAfrican-Americanmen.Discussthegeneralizedissuesthatmayarisefromthisaction.

3. Supposeapopularradiostationconductedatelephonesurveyfrom11:00a.m.to1:00p.m.toevaluatethepopularityofthestationamongthelocalpopulation.Whatistheproblemwiththegeneralizabilityoftheresultsandconclusionsofthisstudy?


section 2: data collection, sampling, and …section 2: data collection, sampling, and experimental...

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