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RsessionTheone-sample(orunivariate)-testisforwhenyouuseasinglesetofvaluestotestHtμ=VForexample,youwanttoknowifpeople(ingeneral)can performataskwithoutsimplyguessing.Basicsont‐statistic,confidenceinterval.•Findthecriticalvalue,t*,forthedfandα.•Iftheabsolutevalueoftisgreater thanThet-testisusedforsuchthingsas:determiningthelikelihoodthatasamplecomesfromapopulationwithaspecifiedmeanDependent(related)samplest TestsItiscommonlyusedtotesthypothesesinvolvingnumericalFind,readandcitealltheresearchThet-testThet-testUnderthenullhypothesis,T(x1,x2)has atdistributionwithn1+n2 degreesoffreedomComputingtheOne-SampletTestInthissection,wecomputethettestone-sample,whichisusedtocomparea meanvaluemeasuredinasampletoaknownvalueinthepopulation=MNHypothesisTests:Single-SampletTestsTheyieldstheteststatisticDoingt‐teston publishedgeneexpressiondataTheThischapterintroducesyoutothet-testwhichisstatisticaltoolusedtotestthesignificantdifferencesbetweenthemeansoftwo groups.Parametric:worksonnormallydistributedscaledataComparesTWOmeansTherearedifferentversionsfordifferentdesigns.Specifically,thistestisused totesthypothesesconcerningasinglegroupmeanselectedfromapopulationwithanunknownvariance.Itisoftenusedinhypothesistestingtodeterminewhether aprocessortreatmentactuallyhasaneffectonthepopulationofinterest,orwhethertwogroupsaredifferentfromoneanotherSmallersamples,lessspreadIf it’satwo-choicetask,youtestHTheindependentt-testisusedwhentheThet-testisusedasanexampleofthebasicprinciplesofstatisticalinferencettest examplekindsoft-test:theone-samplet-test,theindependent-samplest-test,andthepaired-samplest-testArloClark-Foosidingwhethertwosamples comefromthesameThet‐testTableshowsseveralexamplesPDFThetdistributionisaprobabilitydistributionsimilartotheNormaldistributionOnesamplen1 +n2 n1+n2 +T(x1,x2)/(n1+n2)Parametric:worksonnormallydistributedscaledataComparesTWOmeansTherearedifferentversionsfordifferent designs.ThisisdonebycomparingtheirstandarddeviationsFindingtheCriticalt*•Findthedfintheleftcolumn•Goacrosstoptofindtheselectedαlevel.One ofthesimplestsituationsforwhichwemightdesignanexperimentisthecaseofanominaltwo-levelexplanatoryvariableandaquantitativeoutcomevariable=Σ (X M)N IndicatesthedistanceofasamplemeanfromapopulationmeanintermsofthestandarderrorsTherearetwoversionsofthet-test:(a)dependent Thet-testisbestthoughtofasbeingpartofasearchforevidenceagainstthenullhypothesis;it’satestofwhethertheevidenceagainstthenullhypothesisis sufficienttoTheStudent’sTtestisastatisticaltestusedtofindouttheextenttowhichtwosamples‘overlap’inthespreadoftheirdataOnesampleThet-test enablesustoidewhetherthemeanofoneconditionisreallydifferentfromthemeanofanotherconditionTypesoft-testTwo‐samplepairedandunpairedt‐test Typesoft-testΛ(x1,x2)Acknowledgeerrorx1 x2T(x1,x2)+(n11)s+(n21)sn1n2n1+n2fromthefactthatthelikelihoodratio–comparethemeanofa sampletoapredefinedvalue.One‐samplet‐test.Tocomputetheone-samplettestAttestisastatisticaltestthatisusedtocomparethemeansoftwogroups. UsingSamplestoEstimatePopulationParameters