Unit2:Univariate Statistics(Resistant) Unit2PostHole: - - PowerPoint PPT Presentation

• Unit2:Univariate Statistics(Resistant)

Unit2PostHole: ! Unit2TechnicalMemoandSchoolBoardMemo: "! #$! %&%' Unit2(AndUnit3)Reading: (% ")* ")+, "-)%%.,

• Unit2:TechnicalMemoandSchoolBoardMemo

WorkProducts(PartIofII): I. TechnicalMemo:Haveonesectionperbiviariate analysis.Foreachsection,followthisoutline.(2Sections) A. Introduction i. Stateatheory(orperhapshunch)fortherelationship—thinkcausally,becreative.(1Sentence) ii. Statearesearchquestionforeachtheory(orhunch)—thinkcorrelationally,beformal.Nowthatyouknow thestatisticalmachinerythatjustifiesaninferencefromasampletoapopulation,begineachresearch question,“Inthepopulation,…” (1Sentence)

• iii. Listthetwovariables,andlabelthem“outcome” and“predictor,” respectively.
• iv. Includeyourtheoreticalmodel.

B. Univariate Statistics.Describeyourvariables,usingdescriptivestatistics.Whatdotheyrepresentormeasure? i. Describethedataset.(1Sentence) ii. Describeyourvariables.(1ShortParagraphEach) a. Definethevariable(parentheticallynotingthemeanands.d.asdescriptivestatistics). b. Interpretthemeanandstandarddeviationinsuchawaythatyouraudiencebeginstoformapicture

• fthewaytheworldis.Neverlosesightofthesubstantivemeaningofthenumbers.

c. Polishofftheinterpretationbydiscussingwhetherthemeanand standarddeviationcanbe misleading,referencingthemedian,outliersand/orskewasappropriate. C. Correlations.Provideanoverviewoftherelationshipsbetweenyourvariablesusingdescriptivestatistics. i. Interpretallthecorrelationswithyouroutcomevariable.Compareandcontrastthecorrelationsinorderto groundyouranalysisinsubstance.(1Paragraph) ii. Interpretthecorrelationsamongyourpredictors.Discusstheimplicationsforyourtheory.Asmuchas possible,tellacoherentstory.(1Paragraph)

• iii. Asyounarrate,noteanyconcernsregardingassumptions(e.g.,outliersornon9linearity),and,ifa

correlationisuninterpretable becauseofanassumptionviolation,thendonotinterpretit.

• Unit2:TechnicalMemoandSchoolBoardMemo

WorkProducts(PartIIofII): I. TechnicalMemo(continued)

• D. RegressionAnalysis.Answeryourresearchquestionusinginferentialstatistics.(1Paragraph)

i. Includeyourfittedmodel. ii. UsetheR2 statistictoconveythegoodnessoffitforthemodel(i.e.,strength).

• iii. Todeterminestatisticalsignificance,testthenullhypothesisthatthemagnitudeinthepopulationiszero,

reject(ornot)thenullhypothesis,anddrawaconclusion(ornot)fromthesampletothepopulation.

• iv. Describethedirectionandmagnitudeoftherelationshipinyour sample,preferablywithillustrative

examples.Drawoutthesubstanceofyourfindingsthroughyournarrative. v. Useconfidenceintervalstodescribetheprecisionofyourmagnitudeestimatessothatyoucandiscussthe magnitudeinthepopulation.

• vi. Ifsimplelinearregressionisinappropriate,thensayso,brieflyexplainwhy,andforegoanymisleading

analysis. X. ExploratoryDataAnalysis.Exploreyourdatausingoutlierresistantstatistics. i. Foreachvariable,useacoherentnarrativetoconveytheresultsofyourexploratoryunivariate analysisof thedata.Don’tlosesightofthesubstantivemeaningofthenumbers.(1ParagraphEach) ii. Fortherelationshipbetweenyouroutcomeandpredictor,useacoherentnarrativetoconveytheresultsof yourexploratorybivariate analysisofthedata.(1Paragraph) II. SchoolBoardMemo:Concisely,preciselyandplainlyconveyyourkeyfindingstoalayaudience.Notethat,whereasyou arebuildingonthetechnicalmemoformostofthesemester,yourschoolboardmemoisfresheachweek.(Max200 Words)

• III. MemoMetacognitive

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Unit2:RoadMap(VERBAL)

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• Unit1:Roadmap(ROutput)

Unit1 Unit1 Unit2 Unit2 Unit3 Unit3 Unit4 Unit4 Unit5 Unit5 Unit6 Unit6 Unit7 Unit7 Unit8 Unit8 Unit9 Unit9

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• Unit2:Roadmap(SPSSOutput)

Unit1 Unit1 Unit2 Unit2 Unit3 Unit3 Unit4 Unit4 Unit5 Unit5 Unit6 Unit6 Unit7 Unit7 Unit8 Unit8 Unit9 Unit9

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Unit2:RoadMap(Schematic)

• SinglePredictor

ChiSquares ChiSquares Regression ANOVA Polychotomous ChiSquares Dichotomous ChiSquares Logistic Regression Polychotomous Regression ANOVA T9tests Regression Continuous Dichotomous Continuous

Outcome MultiplePredictors

ChiSquares ChiSquares Regression ANOVA Polychotomous ChiSquares Dichotomous ChiSquares Logistic Regression Polychotomous Regression ANOVA Multiple Regression Continuous Dichotomous Continuous

Outcome

Units698:Inferring FromaSampleto aPopulation

3

EpistemologicalMinute

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• Unit2:ResearchQuestion

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• NELS88Math.SavCodebook

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IntrotoStemandLeafPlots(LeadingtoHistograms!)PartIIof IV

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ExploringMathAchievement:LocationandSpread

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AMethodforDetectingUnivariate Outliers(TheRLBandRUB)

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Univariate ExploratoryDataAnalysis

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DigthePostHole

Unit2PostHole: Useexploratorydataanalytictechniquestodescribethedistributionofa variable.

Spread: Scores range from 30 to 71. The midspread is 18.5. The RLB is 15 (43-1.5*18.5) suggesting no lower outliers. The RUB is 90 (61.5+1.5*18.5) suggesting no upper outliers. Location: The median is 51. Shape: The distribution is bimodal.

Evidentiarymaterials:ahistogramandpercentiles. Hereismyshot(theparentheticalcommentsareoptionalbutnice):

Spread:Usethemidspread,min,max,RLBandRUB. Mentionoutliersorthelackthereof. Location:Usethemedian(aka50th percentile). Shape:Ifthedistributionisbimodal(ormultimodal),this factdominates,andskewandkurtosisareprobablynot worthmentioning.Elseifthedistributionisskewed,this factdominates,andkurtosisisprobablynotworth mentioning.Whenthedistributionisunimodal and symmetric, besuretocheckkurtosis(bycomparingtoa normalcurve).

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Dichotomies(andPolychotomies)areEasy!

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• OutlierResistantvs.OutlierSensitiveStatistics

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• ExploringtheEffectofBinSize

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• AnsweringourRoadmapQuestion

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• Unit2Appendix:KeyConcepts

V Donotconfuse“percentagedifferences” with“percentagepointdifferences.” V RuleofThumb#1:RulesOfthumbonlyworkwhentheywork.Useyourown judgment. V Thenormaldistributionisnotparticularlylovedbythegods.Rather,thenormal distributionisaresultofacommonkindofrandomnessresultingfromthe accumulationofmanychanceevents.Itwillplayapivotalroleinthemachinery

• fstatisticalhypothesistesting.

V Forexploratorypurposes,lookwithsofteyes.Wearetryingtoseebeyondthe sampleintothepopulation.It’salittlemystical,Iknow. V Outlierresistantstatisticssuchasthemedianandmidspread canhelpuslook withsofteyes.Theyminimizetheinfluenceofoutliers. V Whenthemedianandthemeandiffer,morethanhalfthesamplewillbeabove

• rbelowaverage(themean).Canyouexplainthattotheschoolboard?(Ithelps

totalkabouttheaverageincomeintheroomandwhathappenswhenBillGates walksthroughthedoor—”TheBillGatesEffect.”) V Donotbefooledbyarbitrarychoicessuchasthesizeofbinsorthelengthof axes.

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• Unit2Appendix:KeyInterpretations

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• 2
• Unit2Appendix:KeyTerminology

V Spread,LocationandShape(SPLASH)::$ %%%16;1;)%$% V Midspread:@ %>4M !$ ! %$ V Median(:% #!) '%!$ ! %$ V Kurtosis: @ V Skew:@ )$$$D V Modality: @% )$C A%B $CA%B V ReasonableUpper/LowerBoundforOutlierDetection(RUB/RLB):@ 1;2> %@16; >% %@!

• 3
• Unit2Appendix:KeyTerminology

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• Unit2Appendix:KeyTerminology(draft)

CategorizingVariables

ModelingPerspective

• Ordinal

V rankings V orderedcategories

• Nominal

V names V unorderedcategories

• Interval

V allunitsareequal V e.g.,(190)=(10– 9)

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• Ratio

V interval V zeromeansnone

Dichotomous

V 2categories

Polychotomous

V ≥3categories

Continuous

V spectrum9like

MeasurementPerspective

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Unit2Appendix:KeyTerminology(Draft)

Continuous Tricky* Dichotomous String Ratio Interval Ordinal Nominal Nominal "

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1 1 60 19 10th Jennifer 57 16 9th Ines 56 15 8th Amy 50 9 7th Shelley 49 8 6th Rachael 48 7 5th Katani 47 6 4th Suzanne 44 3 3rd Kristin 43 2 2nd Josepha 41 1st Meaghan

Modeling: Measurement:

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• Unit2Appendix:SPSSSyntax

*******************************************************************************. *I’m going to produce univariate descriptive statistics and a histogram with a normal curve overlay for the variable MATHACH. */NTILES=4 asks for quartiles. */STATISTICS=STDDEV MINIMUM MAXIMUM MEAN is fairly obvious. */HISTOGRAM NORMAL is also fairly obvious. *Forget about the other lines for now. *******************************************************************************. FREQUENCIES VARIABLES=MATHACH /FORMAT=NOTABLE /NTILES=4 /STATISTICS=STDDEV MINIMUM MAXIMUM MEAN /HISTOGRAM NORMAL /ORDER=ANALYSIS.

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• Unit2Appendix:RSyntax

#------------------------------------------------------------------------------------------------------------------------------ # I’m going to produce univariate descriptive statistics and a histogram for the variable MATHACH.

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• PerceivedIntimacyofAdolescentGirls(Intimacy.sav)

V Source:HGSEthesisbyDr.LindaKilner entitledIntimacyinFemale Adolescent'sRelationshipswithParentsandFriends(1991).Kilner collectedtheratingsusingtheAdolescentIntimacyScale. V Sample:64adolescentgirlsinthesophomore,juniorandseniorclasses

• falocalsuburbanpublicschoolsystem.

V Variables:

,&#&O' @&#&O@' &"$&#&O"' 17$&#&O7' : $&#&O' 1!" $&#&O"' ,; #;O' @; #;O@' &"$; #;O"' 17$; #;O7' : $; #;O' 1!" $; #;O"'

V Overview:Datasetcontainsself9ratingsoftheintimacythat adolescentgirlsperceivethemselvesashavingwith:(a)their motherand(b)theirboyfriend.

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• PerceivedIntimacyofAdolescentGirls(Intimacy.sav)

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• PerceivedIntimacyofAdolescentGirls(Intimacy.sav)

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• PerceivedIntimacyofAdolescentGirls(Intimacy.sav)

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• HighSchoolandBeyond(HSB.sav)

V Source:SubsetofdatagraciouslyprovidedbyValerieLee,Universityof Michigan. V Sample:Thissubsamplehas1044studentsin205schools.Missing data

• ntheoutcometestscoreandfamilySESwereeliminated.Inaddition,

schoolswithfewerthan3studentsincludedinthissubsetofdatawere excluded. V Variables:

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V Overview:HighSchool&Beyond– Subsetofdata focusedonselectedstudentandschoolcharacteristics aspredictorsofacademicachievement.

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• HighSchoolandBeyond(HSB.sav)

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• HighSchoolandBeyond(HSB.sav)

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• HighSchoolandBeyond(HSB.sav)

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• UnderstandingCausesofIllness(ILLCAUSE.sav)

V Source:PerrinE.C.,Sayer A.G.,andWillettJ.B.(1991). SticksAndStonesMayBreakMyBones:ReasoningAboutIllness CausalityAndBodyFunctioningInChildrenWhoHaveAChronicIllness, $%,88(3),608919. V Sample:301children,includingasub9sampleof205whowere describedasasthmatic,diabetic,or healthy.Afterfurtherreductions duetothe%&'%ofcaseswithmissingdataononeormore variables,theanalyticsub9sampleusedinclassendsupcontaining:33 diabeticchildren,68asthmaticchildrenand93healthychildren. V Variables:

#*66":' "D *" #' "D#0%$' #7@' "D7@ #:+' "D:)*& #+01:' "D+1@ #"*' 8:%,)48I #:%' 8:%)48I #,' 8,)48I

V Overview:Dataforinvestigatingdifferencesinchildren’s understandingofthecausesofillness,bytheirhealth status.

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• UnderstandingCausesofIllness(ILLCAUSE.sav)

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• UnderstandingCausesofIllness(ILLCAUSE.sav)

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• ChildrenofImmigrants(ChildrenOfImmigrants.sav)

V Source:Portes,Alejandro,&RubenG.Rumbaut (2001)()$%*"+,- +..)$.BerkeleyCA:UniversityofCaliforniaPress. V Sample:Randomsampleof880participantsobtainedthroughthewebsite. V Variables:

#1'

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8&489%

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"% % V Overview:“CILSisalongitudinalstudydesignedtostudythe adaptationprocessoftheimmigrantsecondgenerationwhichis definedbroadlyasU.S.9bornchildrenwithatleastoneforeign9born parentorchildrenbornabroadbutbroughtatanearlyagetothe UnitedStates.Theoriginalsurveywasconductedwithlargesamples

• fsecond9generationchildrenattendingthe8thand9thgradesin

publicandprivateschoolsinthemetropolitanareasofMiami/Ft. LauderdaleinFloridaandSanDiego,California” (fromthewebsite descriptionofthedataset).

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• ChildrenofImmigrants(ChildrenOfImmigrants.sav)

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• ChildrenofImmigrants(ChildrenOfImmigrants.sav)

>3

• ChildrenofImmigrants(ChildrenOfImmigrants.sav)

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• HumanDevelopmentinChicagoNeighborhoods(Neighborhoods.sav)

V Source:Sampson,R.J.,Raudenbush,S.W.,&Earls,F.(1997).Neighborhoods andviolentcrime:Amultilevelstudyofcollectiveefficacy.$$277,9189 924. V Sample:Thedatadescribedhereconsistofinformationfrom343Neighborhood ClustersinChicagoIllinois.Someofthevariableswereobtainedbyprojectstaff fromthe1990Censusandcityrecords.Othervariableswereobtainedthrough questionnaireinterviewswith8782Chicagoresidentswhowereinterviewedin theirhomes. V Variables: #I%54' I%1554 #&5>' I%155> #,!' ",! #*%%O"'*%% #1' 1 #' 444 #" ' "! #7%' M1<<7% 7 #7' M1<!7

V ThesedatawerecollectedaspartoftheProjecton HumanDevelopmentinChicagoNeighborhoodsin1995.

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• HumanDevelopmentinChicagoNeighborhoods(Neighborhoods.sav)

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• HumanDevelopmentinChicagoNeighborhoods(Neighborhoods.sav)

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• HumanDevelopmentinChicagoNeighborhoods(Neighborhoods.sav)

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• 49HStudyofPositiveYouthDevelopment(4H.sav)

V Sample:Thesedataconsistofseventhgraderswhoparticipatedin Wave3ofthe49HStudyofPositiveYouthDevelopmentatTufts University.Thissubfile isasubstantiallysampled9downversionofthe

• riginalfile,asallthecaseswithanymissingdataontheseselected

variableswereeliminated. V Variables:

#9%' 89%)48& #&' P &D #+' C1+ #,' ,#"' #9* ' 9D !* #'

• #,'

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V 49HStudyofPositiveYouthDevelopment V Source:SubsetofdatafromIARYD,TuftsUniversity

#:"%' C!:%"% #"%' C!"% #"%' C!"% #:' C!: #";' C!";! # <' C<

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• 49HStudyofPositiveYouthDevelopment(4H.sav)

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• 49HStudyofPositiveYouthDevelopment(4H.sav)