z检验与t检验比较区别.

1、Z检验与力检验z test & t test宇传华www. hsta thome comContents l.z test z检验 2. One-sample t test单样本检验 3. Paired-samples t test配对样本/检验 4. Two independent-samples t test两独立样本r检验 5. /test When variances of the two samples areheterogeneous方差不齐时两样本均数厂检验 6. Two type error in hypothesis test假设检验中的两类错误z-distribut

2、ion versus distributionFor very large samples, the test and ztest are identicaloisunknX /iobservat ionX: z = -(3-13)sampleA sampling distribution for “） showing the region ofrejection for a = .05 in a 2-tailed ztest （双狈 检验）A sampling distribution for “） showing the region ofrejection for a = .05 in

3、a 1-tailed ztest （单侧 n 检验）Z = +2.631 One sampleNtest例 根据1983年大址调杳结果，已知某地健康成年男子的脉搏均数为72次/分钟。某医 生2003年在该地随机调査了100名健康成年男子，求得其脉搏均数为74.2次/分钟，标准公 为6.5次/分钟，能否据此认为该成年男子的脉抑数不同于1983年？解：如=72, 2=74.2, n = 100 , S = 6.51.建立假设、确定检验水准a。H : “ =如=72 : “ h “o = 72 , a = 0.052计算检验统计址z =X_-牛=了心打72=3.3846Jn 6.5/J1003确定P

4、值，下结论。資附表】z z00JZ2= 1.96 ,按0=0.05水粧，拒绝 弘 接受，统汁结论为菱别有统计学意义，可认为该地健康男片的脉搏9 1983年不同。A sampling distribution forHoshowing the region ofrejection fora= .05 in a 2-tailed rtest (双狈！JN6 5Z = 3 3&P = 2*(l-noirnsdist (3.38) =0.000795%CI：74.2 1.96-= = (72. 93, 75- 47)VI00洌5-4研究正常人与高血压患者胆固醇含量(mg%)的资料如下，试比较两

5、组血清 胆固醇含量有无差别。正常人组= 506.Fi = 180.6,5, = 34.2高血压组 竹二142,7： = 223.6,5. = 45.81.建立检验假设，确定检验水平比:“严 d ,即正常人与高血压患者血清胆固醇值总体均数相同；,即正常人与高血压患者血清胆固醇值总体均数不同；a = 0. 052计算统计量z值I 180.6 - 223.6 I乙=/-= 10.40V34.22/506 + 45.82/1423.确定P值,作出推断结论本例z =10. 402. 5&故尸故0.05,表明差异无统计学意义按0=0.05水准不拒绝仏，根据 现有样本信息，尚不能认为该地难产儿与一般

6、新生儿平均出生体重不同。例5 1结果图示SS = EX(XX )2I SSExampleX0.2200.2200.2200.2300.2400.2400.2700.2600.2200.240Excel计算方法Excel计算方法（续）Excel result1ABCDE0.220.25230.220. 250.220. 25 t电竺：成对双样本均值分轿40.230. 2550.240. 25飪1260.240. 25平均0. 2360. 2570.270. 25方差0.000315556080.260. 25观测值101010.2220.2230.2240.2350.2460.2470.2780

7、.2690.22100.240. 2S0.250.2S0.250.2S0.250. 250.2S0.250.2S1112131415P-17181920旨入対R 1验践$ASL $AS1052芟昱2 KG墩S假设平均差4）：）：W 0.055ft出竺OO 新工作因姐d）：O斯工作簿而1聿龙1|电肪區90.220. 25泊松招关系数#DIV/0!100.240.25假设平均差011df912t Stat-2.49224148213P（T=t）单尾0.01714782314t单星临界1.83311292315P(T=t)或尽0. 034295&4516t戏尾临舉2.262157158SPS

8、S计算方法Fil* di t ViATrAnsforr 心 0aphs Jftili tis Window H*lpMT 勢图|s| J|C?|仁VAR00001var|24235246.247.278.269.2210.241112134 4ReportsDescriptive Stati.st.icsTablesCompare MeansGeneral Linear ModelMixed ModelsCorrelateRgcnionLQXJ.1UV MXCluxxifzData ReductionScaleHonparajnetr ic TestsTi_me Seri

9、esSurvivalMultiple ResponseMi xing Vidu* AnalyxixCoepL 金 x S AirplATOeans.Independ*nt-Sariples T Test.faired-Samples T Test Qne-ffayANOVA. SPSS计算方法（续）SPSS result95 %CI : - 0.014 2.262 x。淫彳J10应用条件单个样本变量來自随机、独立的正态分布 总体NS，/) 3. Paired-samples t test配对（检验也叫Dependent r-test for paired samples非独立样木/检验This

10、 test is used when the samples are dependent; that is, when thereis only one sample that has been tested twice （repeated measures）or when there are two samples that have been matched or paired适用于非独立囱样本的检验。如每一个 个体被前后测量两次；或两组样本1：1配成对了（按每一 对子的混杂因素（如年龄、性别）配对）。The paired Mest assumes that the differences

11、 between pairs are normallydistributed. If this assumption is violated, it would be better to use:Wilcoxon rank-sign test.（见p79,第九章）d _ pi Difference in the meansSt =- -=- v = / - 1S-=S-standard error y/na配对设计的两种情况同源配对：同一受试对彖作两次不同的处理，或种处理的前后比较异源配对：将受试对象按某些混杂因素（如性别、 年龄、窝别等）配成对子，然后将每对中的两个个 体随机分配给两种处理（

12、如处理组与对照组）优点：配对设计减少了比较对子间的个体差异。特点：资料成对，每对数据不可拆分。介计39!95(J)The number of doses of medication needed for asthmaattacks before and after relaxation trainingH():= 0H 0 oc = 0.05PATIENTWEEK BEFORETRAININGWEEK AFTERTRAININGA94B4IC55D40E5l例5. 2有12名接种卡介苗的儿童，8周后用两批不同的结核菌素，一批是 标准结核菌素，一批是新制结核菌素，分别注射在儿童的前臂，两种结核菌

13、素的皮肤浸润反应平均直径(mm)如表5-1所示，问两种结核菌素的反K5-112名儿扳分朋川购仲H M的皮应性有无差别。H 0 oc = 0.05介计39!95(J)編号标准品；(ftdd2i12.010.02.04.00214.510.04.520.25315.512.53.09.00412.013.0丨01.00513.010.03 09.00612.05.56.542.2574.001.0099.05.55.512.251015.08.07.049.20i 113.06.56.542.251210.59.5!.O1.00=TDIST(4.519,11

14、,2)=0.0009Excel计算方法wwx1孵1分析Clicroxoft Exvelpaired t twst已 文件 AtfiOD Uffitt) Aa)龜衣切IMO)敷爲Q)羽口但) 信期QP MbEd】A Q编号杯)隹品 新制品11210214.5103L5.512.541213513106125.5710.5& 587.5659955101511136.51210.59.5C ,FGHIExcel计算万法与结果ABCD1编号标准品新制品(2_| 112103214.5104 |315.512.55二41213钉513107 _6125.58 1710.58.5987.56.5

15、10995511 1015812 11136.513|1210.595115 I1(11*刁孑方差观测值 泊松相关系数 假设平均差dft StatPg0卑尼t单尾临界P(T=t)或尾t取昆临男标准品新屁品12. 04167 8. 7916675748106 629356112120. 4852420114. 5197980. 0004361. 7958850. 0008722. 20085I e( (D 2的怎坎Q)均隹1) )EBCL) )0(A)：|006納岀顶 出区咬吩)：。 報工作”乂)SPSS计算方法盾国讪I *=l&Sll.Descriptive Slatisties阡Ta

16、blesSPSS计算结果PMi etionSigPair 1VAR00001 & VAR0000212485noPawed Sampler Te$tPaired DlTerenceetdfSig. (2-uiieMeanSW. DelationStd EnorMean9S% Corrtldence ln(9ioioflh DifferenceLxwrUpperF ilc Edi tVi cw DataTransformAntlyreGraphs;1234567891011121314VAR00001 - VAR000023.250002.49089.719061.667364.3326

17、44.52011.00195%CI ：3.25 2.201 x女賈-V12并值的正态性检验(Analyze- DescriptiveStatistics Explore)VARCl111111111I1nn0050oo0oG05o500M5050们1012.131OS.86SCC6 9QVAROOOOIKrcE L :4LVAH：O：33l gG fichcPWs| DatdVK?WX0e- /SPSS Pr&c3%&r ik rudyr*丄心r Jr/rP So ard too*厂tjegsBoocfc*5a 2 心Both*广epend*5 icoe*hi?广Ncrw| G

18、xnu寸Cxtlp RgmapiogaMt$pod Z lovci rMlh J。To共g 1 m需7 6 1888GO3 8603.1 3 6 2 13.HeOCZJED沁心OKEateBeSissies同McUSI-TC5t丈)3P如 S140匕阿e嗨TCme Prw-DescrtXKYEUoffVAWOCXJValidMissingTotalNPercentNPercent忖PercerifVW0000312inn nc*r a* z*dy呛0.05a :心严ur. This i夕a lowf bound ofthtnj勺gnrticQrxQ nLiiliefors Sionrtlcan

19、ce CorrertonKolmogorov* SmirnovfShapiroStSXdfSigstancedfSBVAR0000315400112577Tests of NoiitW法与D法我国国标 GB4882-85 推荐方法，Shapiro-Wilk W 法（1965 年）适用于3 n 50Kolmogorov-Smirnov D 法（？）适用于50 n 1000小于3或大于1000怎么办？ ?）：样本对应的总体服从止态分布编号123456789100.05/2.9 = 2 262表两种方法对d=0.272d d0.2724Sy sj石 _0.1087/yfio JSd=0.087应用条

20、件两变量对子之差來自随机、 独立的正态分 布总体N(0，/)Effect size(效应大小)How large is the effect (the difference)?Coherrs dSquared correlation coefficient (z2)Effect size: Coheres d CoherTs d:d3.25d _=-= 1.305S2.49 Represents mean differenee in standard deviation unitsEffect size: Coheresd Same guidelines for interpreting Co

21、herTs dEffect sizedSmall.80Effect size:P Perce nt of variance explai ned Symbol:PU4.52-=- = 0.29 1 t + df4.52 + 1 1Effect size:P Same guidelines for interpreting z2Effect sizez2Small .25 4. Two independent-samples t test两独立样本r检验应用于：Experimentaltreatment versus control实验砂f究 完全随机设计(completely random d

22、esign)Existing groups一males versus females观察砂疗丄Goal : Assess whether the means of the populations that twodifferent samples came from are the same or different (or whetherone is greater than the other, in a directional test)目的:比较两总体均数是否有差异。应用条件Random and independent samplesNormalityHomogeneity of varianee两组变量值分别来自随机、独立的正态分布总 体N2） 和（“2，b2）且方差相等，即 a,2=a22=T2两独立样本方检验计算公式 S；称为合并方差(combined/pooled variance)洌5.325例糖尿病患者随机分成两组，甲组单纯用药物治疗，乙组采用药物治疗合并饮食疗法，二个月后测空腹血糖(mmol/L)如表5-2所示，问两