统计学中显著水平与P值的区别.doc

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1、UnderstandingHypothesisTests:SignificanceLevels(Alpha)andPvaluesinStatisticsWhatdosignificancelevelsandPvaluesmeaninhypothesistests?Whatisstatisticalsignificanceanyway?Inthispost,I’llcontinuetofocusonconceptsandgraphstohelpyougainamoreintuitiveunderstandingofhowhypothesistestsworkinstatistics.Tobr

2、ingittolife,I’lladdthesignificancelevelandPvaluetothegraphinmypreviouspostinordertoperformagraphicalversionofthe1samplet-test.It’seasiertounderstandwhenyoucanseewhatstatisticalsignificancetrulymeans!Here’swhereweleftoffinmylastpost.Wewanttodeterminewhetheroursamplemean(330.6)indicatesthatthisyear'

3、saverageenergycostissignificantlydifferentfromlastyear’saverageenergycostof$260.Theprobabilitydistributionplotaboveshowsthedistributionofsamplemeanswe’dobtainundertheassumptionthatthenullhypothesisistrue(populationmean=260)andwerepeatedlydrewalargenumberofrandomsamples.Ileftyouwithaquestion:whered

4、owedrawthelineforstatisticalsignificanceonthegraph?Nowwe'lladdinthesignificancelevelandthePvalue,whicharethedecision-makingtoolswe'llneed.We'llusethesetoolstotestthefollowinghypotheses:·Nullhypothesis:Thepopulationmeanequalsthehypothesizedmean(260).·Alternativehypothesis:Thepopulationmeandiffersfr

5、omthehypothesizedmean(260).WhatIstheSignificanceLevel(Alpha)?Thesignificancelevel,alsodenotedasalphaorα,istheprobabilityofrejectingthenullhypothesiswhenitistrue.Forexample,asignificancelevelof0.05indicatesa5%riskofconcludingthatadifferenceexistswhenthereisnoactualdifference.Thesetypesofdefinitions

6、canbehardtounderstandbecauseoftheirtechnicalnature.Apicturemakestheconceptsmucheasiertocomprehend!Thesignificanceleveldetermineshowfaroutfromthenullhypothesisvaluewe'lldrawthatlineonthegraph.Tographasignificancelevelof0.05,weneedtoshadethe5%ofthedistributionthatisfurthestawayfromthenullhypothesis.

7、Inthegraphabove,thetwoshadedareasareequidistantfromthenullhypothesisvalueandeachareahasaprobabilityof0.025,foratotalof0.05.Instatistics,wecalltheseshadedareasthecriticalregionforatwo-tailedtest.Ifthepopulationmea