抽样www.163gg.com

宇传华yuchua@163.
comwww.
hstathome.
com第四章抽样误差与假设检验SamplingErrorandHypothesisTestContents§1.
Samplingerrorofestimatedmean均数的抽样误差§2.
zdistribution&tdistributionz分布与t分布§3.
Estimateofpopulationmean总体均数的估计§4.
Principleandproceduresofhypothesistest假设检验的基本思想与步骤errorsystematicerror(系统误差)avoidablerandomerror随机误差Differencebetweentrueandestimate§1.
Samplingerrorofestimatedmean均数的抽样误差randommeasurementerror随机测量误差randomsamplingerror随机抽样误差----unavoidablestatisticalanalysisdescriptiveinferentialSamplepopulationMean:mSD:sSamplingerror1.
Intervalestimating2.
HypothesestestingSamplingerror↓PopulationsampleSamplemeanPopulationmeanμ≠SamplingerrorsofmeansSamplingerroristhedifferencebetweenthesamplemeanandthepopulationmean,duetothechanceselectionofindividuals.
sampleExampleforsamplingerrorofmean将这100份样本的均数看成新变量值,按第二章的频数分布方法,得到这100个样本均数的直方图如下:CentralLimitTheorem中心极限定理1)IfX~N(μ,σ2),then2)IfX~N(μ,σ2),whennislargeenough,n≥30or50islargeenoughingeneralButifXisstronglyskewness,samplesizesshouldbemorelarge.
中心极限定理:当样本含量足够大的情况下,无论原始测量变量服从什么分布,的抽样分布均近似正态.
抽样分布条件样本含量足够大sStandardErroroftheMean(SEM)均数的标准误Thisequationimpliesthatsamplingerrordecreasesassamplesizeincreases.
Thisisimportantbecauseitsuggeststhatifwewanttomakesamplingerrorassmallaspossible,weneedtouseaslargeofasamplesizeaswecanmanage.
Samplesize(n)图不同样本含量时的均数分布例4.
1在某地随机抽查成年男子140人,计算得红细胞均数4.
77*1012/L,标准差0.
38*1012/L,试计算均数的标准误.
标准误是抽样分布的重要特征之一,可用于衡量抽样误差的大小,更重要的是可以用于参数的区间估计和对不同组之间的参数进行比较.
SD():Itdescribesthedispersionoftheobservationsfromthemean.
usedinthedescriptiveanalysisSE():Itdescribesthedispersionofthesamplemeansfromthepopulationmean.
usedintheinferentialanalysisThedifferencebetweenSD&SE§2.
zdistribution&tdistributionpopulationsample1sample2sampler……t-distributionCharacteristicsoft-distributionThedensityfunctionissymmetryaboutt=0;Whent=0,densityfunctionhasmaxvalue;Thereareaclusterofdensityfunctionswithdifferentdegreeoffreedomν,thesmallertheν,thedispersedthet-values,thelargertheν,thedensityfunctionmoreclosertothenormaldistribution.
Whenν=∞,t-distributionfunctionisidenticalwiththenormaldistributionfunction.
Theareaunderthecurveis1.
(p195)Tablefort-criticalvalues(p195,附表2)0t-tα/2α/20t-tα01.
96-1.
96.
05/2.
05/2(ν=∞)01.
64-t0.
05(ν=∞)one-tail单侧two-tail双侧01.
64-t0.
05(ν=∞)Ex1:Forgivenprobabilityαanddf,findoutthecriticalvaluest(α,df).
由P值,df获得t临界值t0.
05/2,20=t0.
05/2,50=t0.
05/2,∞=0t-t01.
96-1.
96.
05/2.
05/22.
0862.
0091.
9601.
7251.
6761.
645(ν=∞)t0.
05,20=t0.
05,50=t0.
05,∞=(p195,附表2)=TINV(0.
05,20)=TINV(2*0.
05,20)=NormsINV(0.
05/2)=NormsINV(0.
05)Ex2:Forgivencriticalvaluesanddf,findouttheprobabilityinterval.
由t、df获得P值t≥1.
85,ν=10t≤-1.
85,ν=10|t|≥1.
85,ν=100.
025μ0都有可能H1:μ>μ0,单侧H1:μ<μ0,单侧对于本例,根据医学知识,经常参加体育锻炼的中学男生心率不会高于一般中学男生的心率.
所以使用单侧.
即H0:μ=μ0,H1:μ<μ0由专业知识确定单、双侧.
假设检验中α与P有何不同α事先确定的界值.
有统计学意义的最大P值.
所谓P值,是指在H0成立的前提下,出现目前样本数据对应的统计量(如z、t、F值等)数值乃至比它更极端数值的概率.
P值也是一个随机变量.
1.
96P=0.
05-1.
96z0f(z)