T检验U检验课件

9.4ttestandutest

Hypothesistestingforpopulationmean

Example:Hemoglobinof280healthymaleadultsinaregion:Question:Whetherthepopulationmeaninthisregionis140.0g/L?Twopossibilities:

(1)Thepopulationis140,thesamplemean=136.0isduetothesamplingerror

(Nullhypothesis)

(2)Thepopulationisnot140atallsothatthesamplemean=136.0

(Alternativehypothesis)

Question:Whichisthetruth?

--problemofhypothesistest!

Basiclogic:

Underthenullhypothesis

Howpossibletooccurthecurrentsituationandevenmoreunfavorablesituationto

?--Calculateaprobability(-value)Ifitislesspossibletooccurthecurrentsituationandevenmoreunfavorablesituationto,thenreject;otherwise,notreject.

--Givenasmall,compareand

(iscalledthelevelofthetest)Example9-15:Thecontent(mg/L)ofwithinamaterialwasindependentlymeasured15times,resultingin:

20.99,20.41,20.62,20.75,20.10,20.00,20.80,20.91,22.60,22.30,20.99,20.41,20.50,23.00,22.60.Pleasecheckwhetherthetruevaluewas20.7mg/L.1.ComparingtoagivenpopulationmeanCaCo3

SethypothesesandtheleveloftestTomakedecision:rejectoraccept?Ifreject,theprobabilityofmissrejectshouldnotbegreaterthan.(2)Selectanappropriatetestandcalculatetheteststatistics

IfXfollowsanormaldistributionThenWhenholds,Basedonthecurrentsample:

(3)DeterminePvalue,andmakedecisionWhenholds,theprobabilityofthecurrentsituation(samplemean=21.13)andevenmoreunfavorablesituation(samplemean>21.13)toisgreaterthan0.05.TheprobabilityofthecurrentsituationandevenmoreunfavorablesituationtoiscalledPvalue.NowP>,noreasontoreject.2.ComparisonforPairedDataExample9-13(Apaireddesign)8patientswithhypertensionweretreatedwithamedicineandtheDBPwasmeasuredbeforeandafterthetreatment.Datalistinthetable9-10.

α=0.05

υ=8-1=7

t>t0.05,7=2.365,P<0.05,isrejectedatsignificancelevelα=0.05.

3.ComparisonbetweenTwoSampleMeans

Example9-18:Twogroupofratswerefedbydifferentfood.Onecontainshighprotein,anothercontainslowprotein.Comparingtheeffectsofdifferentfoodonincreasingweight.α=0.05Thepooledestimationofsamplevarianceisυ=n1+n2-2=12+7-2=17

P>0.05,thenullhypothesisisnotrejectedatthesignificancelevelα=0.05.a.WhatdoesP-valuemean?

P-valueistheareaofthetail(s)inthedistributionoftheteststatisticbeyondthevalue(s)oftheteststatisticcalculatedbasedonthesample.Ifthenullhypothesisisrejected,theprobabilityofmistake=P--AsmallerP-valueimpliesthebetterqualityofyourrejection.Ifthenullhypothesisisnotrejected,thebiggerP-valueimpliesthebetterqualityofyouracceptation.4.AttentionforHypothesisTest

b.Whatdoesthesignificancelevelαmean?

αshowsthequalityoftheinference.

Ifyourejectthenullhypothesis,theprobabilityofmakingmistake