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TRIOLA:WHAT’SHOT/NOT
Statisticalmethodsweteacharegettingclosertothoseusedbyprofessionalstatisticians.
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HOT!
TRIOLA:WHAT’SHOT/NOT
StatisticalMethodsNo: “Usezifn >30”
• Journals/professionals:Almostnever• Technologynowmakest easy
NOT!
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TRIOLA:WHAT’SHOT/NOT
StatisticalMethodsConfidenceIntervalandHypothesisTestfor𝛍 assumingknown𝛔
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• Unrealistic!• Journals/professionals:never• Technology:t easy
NOT!
TRIOLA:WHAT’SHOT/NOT
• Journals/professionals:almostnever• Procedure:H0 with=only
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H0 with ≥ or ≤StatisticalMethods
NOT!
TRIOLA:WHAT’SHOT/NOT
Confidenceintervalandhypothesistestfortwo independentmeans with
1.Knownstandarddeviationsor 2.Equalstandarddeviations
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StatisticalMethods
NOT!
TRIOLA:WHAT’SHOT/NOT
TwoIndependentMeans2knownstandarddev’s:unrealistic
Assumingequal standarddev’s:pooling• OKinplacebo/treatmentgroups• Yieldshigherdf,sogreaterpowerand/ornarrowerconfidenceinterval
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TRIOLA:WHAT’SHOT/NOT
ConfidenceIntervalforp using…• Plus4• Score
insteadofWald(straightnormalapproximationtobinomial)
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HOT!
TRIOLA:WHAT’SHOT/NOT
1.Askaresearchquestion.2.Designastudyandcollectdata.• Dean’ssurvey• Subwaysurvey• “AlwaysstateclaimasH1”• Bayer:“325mgaspirin”
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Inreality,itisoftenimpossibleto…
TRIOLA:WHAT’SHOT/NOT
Teachusing…• Realclaims• Realdata• Statisticalmethodsusedbyprofessionals
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HOT!
TRIOLA:WHAT’SHOT/NOT
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PrintedTablesNOT!
TRIOLA:WHAT’SHOT/NOT
Technology“Anyscientificcalculator”• Failtodeveloptechnologyskills• Toomuchfocusoncalculationmechanics
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NOT!
TRIOLA:WHAT’SHOT/NOT
• TI-83/84Plus• Statdisk• Excelwithadd-in:XLSTAT• StatCrunch• Minitab• SAS,JMP,SPSS• R,Fathom,Stata,Statistica,…
TechnologyHOT!
TRIOLA:WHAT’SHOT/NOT
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Product Cost OperatingSystem
AllowsSummaryStatistics?
UserFriendly?
TIcalculator $86 TI-83/84Plus$120TI-84 PlusCE
YES YES
STATDISK Freetoadopters Win/Mac YES YES
StatCrunch $12 individualor$5bundled
Internet YES YES
Minitab $30rent6months$14bundled
Windows only YES YES
Excel $59(often“free”)plus$10XLSTATadd-inorXLSTAT freebundled
Win/Mac NO SOMEWHAT
SPSS $40rent6monthsor$20Bundled
Win/Mac NO NO
JMP(fromSAS) $30 rent6MonthsFreebundled
Win/Mac NO NO
SAS Free Win/Mac NO NO
Technology
TRIOLA:WHAT’SHOT/NOT
1.Numbercrunching• Focusonunderstandingandinterpreting
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Technology
2.ProfessionalGraphs:PDD!Technologyfor…• Histograms• Scatterplots• NormalQuantilePlots
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HOT!
TRIOLA:WHAT’SHOT/NOT
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r=0.816;P-value=0.002
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r=0.816;P-value=0.002
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r=0.816;P-value=0.002
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r=0.816;P-value=0.002
TRIOLA:WHAT’SHOT/NOT
• P-ValueMethod• CriticalValueMethod• ConfidenceIntervalMethod• Simulations!!!
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HypothesisTesting
TRIOLA:WHAT’SHOT/NOT
3.Technology:SimulationsExample:SimulationforHypothesisTestTestclaimμ =98.6usingn=106,=98.2,s=0.62
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HOT!
x
TRIOLA:WHAT’SHOT/NOT
Claim:Meanbodytemp=98.6degrees.
SampleData:n=106=98.20
s=0.62
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Simulation:HypothesisTests
x
TRIOLA:WHAT’SHOT/NOT
98.7086 98.5790 98.6065 98.513498.6417 98.6801 98.6459 98.549098.5726 98.5512 98.5219 98.615798.7668 98.5900 98.5051 98.5980
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Simulation:HypothesisTests
TRIOLA:WHAT’SHOT/NOT
4.Tech:BootstrapAlcohol(sec)invideogames(JAMA):841458350057207431780257
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HOT!
TRIOLA:WHAT’SHOT/NOT
StatisticsCurriculum
Crammingintoomanytopics
inclass
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NOT!
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5.TechforNewTopicsExample:Aftercoveringhypothesistestswithonepopulation,assignexercisesthatinvolvetwopopulations.
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HOT!
TRIOLA:WHAT’SHOT/NOT
Normalapproximationtobinomial
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NOT!
TRIOLA:WHAT’SHOT/NOT
6.TechforExactResults
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HOT!
TRIOLA:WHAT’SHOT/NOT
Footballovertimecointoss:• 431overtimecointosswinners• 235winsbythoseteams• IsP(win)>0.5(ifcointossiswon)?
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RealExample
TRIOLA:WHAT’SHOT/NOT
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Testingp>0.5
TRIOLA:WHAT’SHOT/NOT
Assumingp =0.5:P(235+wins)=0.0335332
Because235winsissignificantly high,cointosswinnershaveanadvantage.
Interpretation:Changetherule!
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Testingp>0.5
TRIOLA:WHAT’SHOT/NOT
7.Technology for…
Every2minutesnow:Asmuchdataasfrombeginningoftimetotheyear2000
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HOT!
TRIOLA:WHAT’SHOT/NOT
Usesome
BIGdatasets!
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BIG
TRIOLA:WHAT’SHOT/NOT
Checkrequirements!
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Requirements
“Assumenormaldist.”
HOT!
NOT!
TRIOLA:WHAT’SHOT/NOT
Requirements
Normalquantile plottochecknormality
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HOT!
TRIOLA:WHAT’SHOT/NOT
Technology:Easy
Normalif…1. Pointsclosetostraightline2. Nononlinearpattern
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NormalQuantilePlot
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Normal:IQScores
TRIOLA:WHAT’SHOT/NOT
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NotNormal:Pattern
TRIOLA:WHAT’SHOT/NOT
JournalofBasicandAppliedSocialPsychology:
“AcceptnoarticlesthatincludeP-values”
Because…• P-values:excuseforlowerqualityresearch• P-valuebaristooeasytopass• P-valuesyieldbinaryconclusions
P-valueandNHSTControversy
TRIOLA:WHAT’SHOT/NOT
• Samplesize(small/big)• Power• Practicalsignificance• Effectsize• C.I.,OR,RR,replication,…
SupplementNHSTwith…
TRIOLA:WHAT’SHOT/NOT
ClinicalTrialSuccessRatesSurgery: 67/73=92%Splints: 60/83=72%
P-Value=0.000896Surgeryisbetter!
Example:CarpalTunnel
TRIOLA:WHAT’SHOT/NOT
95%CI: 8%<p1‒p2 <31%
Splint/surgeryforfailure:• OddsRatio
4.28(1.6<OR<11.2)• Power=0.80(for20%difference)
Therestofthestory…
TRIOLA:WHAT’SHOT/NOT
• Useseveralapproaches:Parametric,nonparametric,bootstrap,simulation
• Severalmethods:H.T.,C.I.,Power,OR,RR
• Replicate• PracticalSignificance
Ifanalysisisimportant…
TRIOLA:WHAT’SHOT/NOT
Evaluatingformulas!
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NOT!
TRIOLA:WHAT’SHOT/NOT
BeyondtheFormula:ConceptualUnderstanding
Developsense,understanding,andinterpretation ofstandarddeviation:• Chebyshev’sTheorem: Toocrude;skipit.• EmpiricalRule: Coveredlater;skipit.
Rangeruleofthumb“Significant”results:Beyondthemean± 2standarddeviations
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TRIOLA:WHAT’SHOT/NOT
• IsanIQof135significantlyhigh?(Givenμ =100andσ =15)
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• Estimates forheightsofstudentsinclass:
s ≈range/4
BeyondtheFormula:ConceptualUnderstanding
TRIOLA:WHAT’SHOT/NOT
GoBeyondtheFormula
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P(A orB)=P(A)+P(B)−P(AandB)
Usecommon-senserule:TofindtheprobabilityofAorB:Addwithoutdouble-counting.
HOT!
NOT!
TRIOLA:WHAT’SHOT/NOT
Findtheprobabilityofapositiveresultoralie.
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TruthTold LieToldPositivePolygraph
15(false positive)
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NegativePolygraph
32 9(falsenegative)
Addwithoutdouble-counting
TRIOLA:WHAT’SHOT/NOT
ProbabilitySimulations• Birthdayproblem• 200coins:real/fake
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HOT!
TRIOLA:WHAT’SHOT/NOT
ProbabilityPermutations&Combinations:• Do lotterydemo• Don’tusevaluabletime
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NOT!
Interpret ResultsBad:Findprobabilityof20headsin20tossesofacoin.
Good:Ifamethodofgenderselectionhasnoeffect,whatistheprobabilityofgetting20girlsin20births?Doestheresultsuggestthatthemethodiseffective?Whyorwhynot?
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HOT!
TRIOLA:WHAT’SHOT/NOT
Tovastly improveastatisticscourse,...
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Really HOT!
TRIOLA:WHAT’SHOT/NOT
Projects• Groupsof3or4• Oralpresentationbyall• Computerprintout• Briefwrittenreport
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HOT!
TRIOLA:WHAT’SHOT/NOT
Beyondteachingstastistics,wecanhelpourstudentsgrow throughdeveloping…
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Educating(notjustteaching)
TRIOLA:WHAT’SHOT/NOT
• Criticalthinking• Technology• Collaboration• Speaking
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ImportantLifeSkills
TRIOLA:WHAT’SHOT/NOT
Threekeyfeatures:1. Technology2. Technology3. TechnologyPlus…
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FutureofStatCoursesHOT!FutureofStatCourses
TRIOLA:WHAT’SHOT/NOT
• Routine activeinvolvement• Real projects• Bigdatasets
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HOT!FutureofStatCourses
TRIOLA:WHAT’SHOT/NOT
•Moretopics(viatechnology)• Bettertechnology• Studentsmorestatsavy
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HOT!FutureofStatCourses
• PrintedTables• Normalapprox.tobinomial• “Assumenormaldist.”• Knownσ• Manualcalculations• P-valuesalone• Combinatorics
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• Technology• Checkrequirements• Plotthedata• Holisticapproach• Bigdata• Bootstrapping• Simulations• Interpret results• Userealdata• Projectsandactivities
HOT! NOT!
TRIOLA:WHAT’SHOT/NOT
•Activeinvolvement•Projects• Technology
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HaveFun!!!HOT!
