STATISTICAL METHODS WITH SAS PROGRAMMING
STATISTICAL METHODS WITH SAS PROGRAMMING STAT 6623
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This 2 page Class Notes was uploaded by Miss Genesis Rath on Friday October 2, 2015. The Class Notes belongs to STAT 6623 at Arkansas State University taught by Staff in Fall. Since its upload, it has received 36 views. For similar materials see /class/217737/stat-6623-arkansas-state-university in Statistics at Arkansas State University.
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Date Created: 10/02/15
STaT 6623 STaTisTical MeThods wiTh 5A5 Programming More on hypoThesis TesTing adapTed from InTro STaTs by Richard DeVeaux and Paul Velleman Addison Wesley HypoThesis TesTing is very much like a courT Trial Suppose The defendanT has been accused of robbery We wonder wheTher he is guilTy or noT In US law The null hypoThesis is ThaT The defendanT is innocenT InsTrucTions To juries are expliciT abouT This In The Trial The prosecuTor gaThers and presenTs evidence This evidence Takes The form of facTs ThaT seem To conTradicT The presumpTion of innocence If The defendanT were innocenT wouldn39T iT be remarkable ThaT The police found him aT The scene of The crime wiTh a big bag of money in his hand a mask on his face and a geTaway car parked ouTside The nexT sTep is To judge The evidence The jury considers The evidence in lighT of The presumpTion of innocence and judges wheTher The evidence againsT him would be plausible if The defendanT were in facT innocenT We ask Could These daTa plausibly have happened by chance if The null hypoThesis were True If They were very unlikely To have occurred Then The evidence raises reasonable doubT in our minds abouT The null hypoThesis If The evidence is noT sTrong enough To rejecT The defendanT39s presumpTion of innocense whaT verdicT does The jury reTurn They say quotnoT guilTy They do noT say The defendanT is innocenT All They say is They have noT seen sufficienT evidence To convicT rejecT innocence The jury39s null hypoThesis is H0 innocenT defendanT If The evidence is Too unlikely given This assumpTion The jury rejecTs The null hypoThesis and finds The defendanT guilTy If There is insufficienT evidence To convicT The defendanT The jury does noT decide ThaT H0 is True and declare him innocenT RaTher juries can only fail To rejecT The null hypoThesis and declare The defendanT noT guilTy In The same way if The daTa are noT parTicularly unlikely under The assumpTion ThaT The null hypoThesis is True Then The mosT we can do is To fail To rejecT The null hypoThesis We never declare The null hypoThesis To be True because we simply do noT know wheTher iT39s True or noT SomeTimes in This case we say The null hypoThesis has been reTained More on p value adapTed from The Basic PracTice of STaTisTics by David Moore Freeman SomeTimes we demand a specific degree of evidence in order To rejecT The null hypoThesis We can compare The p value wiTh a fixed value ThaT we regard as decisive This amounTs To announcing in advance how much evidence againsT H0 we will insisT on When There is a decisive value of p value iT is called The significance level and we wriTe iT as 0 For example when 0 is seT aT 05 we require evidence againsT H0 so sTrong ThaT iT would happen no more Than 5 of The Time when H is True When we seT 0 01 we are insisTing on sTronger evidence againsT H0 evidence so sTrong ThaT iT would appear only 1 of The Time if H is in facT True If The p value is as small or smaller Than X we say ThaT The daTa are sTaTisTically significanT aT level 0 STaTisTically significanT does noT mean imporTanT iT simply means noT likely To happen by chance How small a p value is convincing evidence againsT H0 The answer depends mainly on Two circumsTances How plausible is H0 If H represenTs an assumpTion ThaT The people you musT convince have believed for years sTrong evidence small p value will be needed To persuade Them WhaT are The consequences of rejecTing H0 If rejecTing H0 in favor of HG means making an expensive change you need sTrong evidence ThaT making The expensive change will be beneficial There is no sharp border beTween significanT and insignificanT only increasingly sTrong evidence as The p value decreases IT makes no sense To TreaT p value 05 as a universal rule for whaT is significanT
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