Sociology 301 Hypothesis Testing - Sites.Udel.Edu · Sociology 301 Hypothesis Testing ... Be able to state hypotheses in words and symbols. ... Choose an alpha level and iden7fy the

Sociology 301

Hypothesis Testing

LiyingLuo

04.12

Why You Should Care

1.Makeareasonable/ra7onaldecision.

2.Desirableskillsonthejobmarket.

The Scope and Objectives of this Class

Whatisthisclassallabout?

methodsandsta7s7cs

Theobjec7ves:

“howsta7s7csarecomputedandinterpreted,andhowtheycanbeusedtoaddresskeysocialscienceques7ons.”

Unsolicited Advice

Itisahardclass…

However,youcansucceedbyworkinghard…

Our Goal

Theunknown“truth”…

popula7onparameters(e.g.,mean,propor7on)

Makeagood(i.e.,informed)guess…

usingsample(e.g.,samplemean,samplepropor7on)

CI for Proportion

Schlitzvs.Michelob:WhywasSchlitzsosurethattheresultsairedliveatSuperBowlhalSimewouldnotscrewthem?

Thesebeerstastenodifferent:

AccordingtoCLT:

Forn=100,95%CI?99%CI?

Terminology

Population Parameter

Sample Statistic

Sampling Distribution

mean

variance

standard deviation

Hypothesis Testing

Are all swans white?

Hypothesis Testing

Hypothesis:Claims(abouttruth,popula7onparameters)

Thelogicoffalsifica7on:webestadvanceknowledgebydisapprovinghypotheses.

i.e.,cannotapprove,butcondi7onallyaccept

Hypothesis Testing

Thebasicques7on:

Whatistheprobabilityofge]ngasamplesta7s7cifthetruepopula7onparameterhasahypothesizedvalue?

Isthesampleevidencesufficienttomakeconfidentconclusionsaboutthepopula7on?

So,hypothesisisalwaysaboutpopula7onparameters,althoughwetesttheirtruevalueswithasamplesta7s7c.

Hypothesis Testing

TaylorSwiS’s“BlankSpace”

Hypothesis Testing

TaylorSwiS’shypothesisin“BlankSpace”:

“Boysonlywantloveifit’satorture.”

Howcanwetestthishypothesis?

Hypothesis Testing: Steps

1.Stateyournullandresearchhypotheses

2.Decidethealphalevelandcri7calvalue

3.Computetheteststa7s7c

4.Comparetheteststa7s7ctothecri7calvaluetomakeadecision

5.Stateatechnicaldecisionandasubstan7veconclusion

Hypothesis Testing: 1. State hypotheses

Hypothesiscomesinpairs.

H1:ResearchHypothesis…stateswhatyoubelievetobetrue.

H0:NullHypothesis…statestheoppositeofH1;astatementthatyouexpecttorejectasuntrue.


Twotypesofhypothesis

Type1:Hypothesessta7ngthedirec6onofapopula7onparameter

One-sidedhypotheses

H0:UDelmeanGPAisbelow3.00

H1:UDelmeanGPAis3.00orhigher

Type2:Hypothesesuncertainaboutthepopula7onparameter’sdirec7on

Two-sidedhypotheses

H0:UDelmeanGPAis3.00

H1:UDelmeanGPAisnot3.00

H0: μ<3.00 H1: μ≥3.00

H0: μ=3.00 H1: μ≠3.00


Beabletostatehypothesesinwordsandsymbols.


TaylorSwiS’shypothesisin“BlankSpace”:

“Boysonlywantloveifit’satorture.”

Let’shelpherdeveloparesearchhypothesisandanullhypothesis.


TaylorSwiS’sresearchhypotheses:

H1:90%ormoreyoungmen,agedbetween16and28,intheUSonlywantloveifit’satorture.

H0:Lessthan90%youngmen,agedbetween16and28,intheUSonlywantloveit’satortureornot.

H0: μ<0.9 H1: μ≥0.9


AresearcherhypothesizesthatintheUnitedStatestheaverageyearsofschoolingforwomenisgreater12years.

Statethenullandresearchhypothesesinwordsandsymbols.

H0:?

H1:?


AresearcherhypothesizesthatintheUnitedStatestheaverageyearsofschoolingforwomenisnotequalto12years.


H0:?

H1:?


Aresearcherhypothesizesthatthemeanannualsalaryofadefec7veislessthan$75,000.


H0:?

H1:?


Aresearcherhypothesizesthatthemeanannualsalaryofadefec7veisnotequalto$75,000.


H0:?

H1:?


AresearcherhypothesizesthatintheUnitedStatesthemeannumberofsexthatadultsyoungerthan40yearsisgreaterthan1007mesperyear.


H0:?

H1:?


AresearcherhypothesizesthatintheUnitedStatesthemeannumberofsexthatadultsyoungerthan40yearsisnotequalto1007mesperyear.


H0:?

H1:?

Hypothesis Testing

Twopossibledecisions:

rejec7ngthenullhypothesis

or…

acceptthenullhypothesis?

Hypothesis Testing

Twopossibledecisions:

rejec7ngthenullhypothesis

or…

acceptthenullhypothesis?failtorejectthenullhypothesis

Errors in Hypothesis Testing

Wealwaysruntheriskofmakinganincorrectdecision,whateverdecisionwemaymake.


Wealwaysruntheriskofmakinganincorrectdecision,whateverdecisionwemaymake.

Soweneedtoacknowledgeandmakeitexplicitaboutthehowmucherrorwewouldliketorisk.


IfthenullhypothesisH0isinfacttrue,butwerejectit:

TypeIError

IfthenullhypothesisH0isinfactfalse,butwefailtorejectit:

TypeIIError

Scien7stscareabout…orareobsessedwith…TypeIError.

Thatis,wewouldliketohaveasmallα.


TypeIError…orFalseRejec7onError…occurswhenweincorrectlyrejectatruenullhypothesis.



ThemeanGPAis3.20inaoursample,sowedecidetorejectH0.

However,themeanGPAis2.90isinfactinthepopula7on,soourdecisiontorejectH0isanerror.

H0: μ<3.00 H1: μ≥3.00

Alpha (α)

TheprobabilityofmakingTypeIErrorisdenotedbyα

P(TypeIError)=α

…alphalevel,alphaarea,orregionofrejec6on

One-tailhypothesisTwo-tailhypothesis

Alpha (α)

Thepreciseα levelweselectisarbitrary,andvariesbydiscipline(andsome7mesbyjournalorevenbyauthor).

0.05ismostcommon.

0.01isalsoverycommon.

Critical Value


Cri6calValue:theminimumvalueofadistribu7onnecessarytodesignateanalphaarea,i.e.,howlargetheteststa7s7cmustbeinordertorejectthenullhypothesisatthegivenalevel.

Critical Value


Cri6calValue:theminimumvalueofadistribu7onnecessarytodesignateanalphaarea,i.e.,howlargetheteststa7s7cmustbeinordertorejectthenullhypothesisatthegivenalevel.

Critical Value

Cri7calvaluesformanydistribu7ons:

Z,t,F,…

Hypothesis Testing: 2. Choose an alpha level and determine the critical value

Thecri7calvaluethatyouwilluseinhypothesistes7ngdependsonyourchoiceofalphalevelandthetypeofhypothesis(one-tailvs.two-tail)

Zαdenotesthecri7calvalueforaone-tailedtest.

Zα/2denotesthecri7calvalueforatwo-tailedtest.

Chooseanalphalevelandiden7fythecri7calvalueforthefollowingtests…



H0:UDelmeanGPAisnotequalto3.00


H0: μ<3.00 H1: μ≥3.00

H0: μ≠3.00 H1: μ=3.00

Hypothesis Testing: 3. Compute a test statistic

Supposethatthestandarddevia7onforthepopula7onisσ=0.5.

WhatistheZ-scoreofasamplemean=3.2withsamplesizen=100?





H0: μ<3.00 H1: μ≥3.00

H0: μ=3.00 H1: μ≠3.00

Hypothesis Testing: 4. Make a decision by comparing the test statistic to the critical value

Rule:rejectH0iftheabsolutevalueofyourteststa7s7cislargerthanthecri7calvalue|Z|>Zα/2orZα

One-tail

Two-tail

Hypothesis Testing: 4. Make a decision by comparing the test statistic to the critical value

Rule:rejectH0iftheabsolutevalueofyourteststa7s7cislargerthanthecri7calvalue|Z|>Zα/2orZα







H0: μ<3.00 H1: μ≥3.00

H0: μ=3.00 H1: μ≠3.00

Hypothesis Testing: 5. State your conclusion

Technically:Atthatalphalevel,werejectorfailtorejectH0.

Substan7vely:Atthatalphalevel,wedoordonotsufficientevidencetoconcludethat…







H0: μ<3.00 H1: μ≥3.00

H0: μ=3.00 H1: μ≠3.00

Hypothesis Testing: Steps






Example 1

In2007theU.S.Na7onalTransporta7onSafetyBoardseta5-yeargoalofhavingmorethan95%ofallAmericandriversusetheirseatbelts.

Toseewhethertheyareontargetformee7ngthatgoal,theyrandomlysampled1,000Americandriversin2012.

Theyfoundthat962—or96.2%—ofthe1,000driverstheysampledusetheirseatbelts






Example 2

Aveterinarianclaimsthat6%ofcatshaveFIDS(FelineImmuneDeficiencySyndrome).

Toevaluatethisclaim,researchersrandomlysampled320catsTheyfoundthat26—or8.1%—ofthe320catshaveFIDS.

Isthisevidencesufficienttoconfidentlyconcludethatthepopula7onpropor7onofcatswhohaveFIDSisdifferentfrom0.06?






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Sociology 301 Hypothesis Testing - Sites.Udel.Edu · Sociology 301 Hypothesis Testing ... Be able to state hypotheses in words and symbols. ... Choose an alpha level and iden7fy the