统计学30个重点及例题分析

1、统计学例题操作分析（仅供参考） 1.单样本t检验（样总t检验）P55L4-7 SPSS操作主要结果（1）进行正态性检验Tests of NormalityKolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.M物质.1449.200*.9649.840a. Lilliefors Significance Correction*. This is a lower bound of the true significance.（2） 进行单样本t检验One-Sample TestTest Value = 63.5 tdfSig.

2、(2-tailed)Mean Difference95% Confidence Interval of the DifferenceLowerUpperM物质-45.1428.000-21.13333-22.2129-20.05382.配对t检验（异体配对/自身前后、左右配对）P57L4-8 SPSS操作主要结果（1） 先计算配对差值d再对d进行正态性检验Tests of NormalityKolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.d.19310.200*.96310.819a. Lilliefors Signif

3、icance Correction*. This is a lower bound of the true significance.（2） 进行配对t检验Paired Samples CorrelationsNCorrelationSig.Pair 1对照 & 实验10.075.838Paired Samples TestPaired DifferencestdfSig. (2-tailed)MeanStd. DeviationStd. Error Mean95% Confidence Interval of the DifferenceLowerUpperPair 1对照 - 实验2.16

4、0001.32094.417721.215053.104955.1719.0013. 两独立样本t检验（成组t检验） P59L4-9 SPSS操作主要结果（1）进行正态性和方差齐性检验Tests of Normality观察对象Kolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.转铁蛋白含量正常人.11612.200*.98612.998患者.14715.200*.92715.245a. Lilliefors Significance Correction*. This is a lower bound of the tru

5、e significance.Test of Homogeneity of VarianceLevene Statisticdf1df2Sig.转铁蛋白含量Based on Mean1.877125.183Based on Median1.127125.299Based on Median and with adjusted df1.127122.304.300Based on trimmed mean1.798125.192（2）再做成组t检验Independent Samples TestLevenes Test for Equality of Variancest-test for Eq

6、uality of Means95% Confidence Interval of the DifferenceFSig.tdfSig. (2-tailed)Mean DifferenceStd. Error DifferenceLowerUpper转铁蛋白含量Equal variances assumed1.877.1837.40225.00036.66004.952826.459546.8605Equal variances not assumed7.67524.795.00036.66004.776426.818646.50144.完全随机设计资料ANOVA与多重比较 P69L5-2 S

7、PSS操作主要结果（1） 正态性和方差齐性检验Tests of Normality药物Kolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.E-SFC对照组.1799.200*.9479.653淫羊霍.13610.200*.95610.739党参.19710.200*.92310.380黄芪.15110.200*.95210.692a. Lilliefors Significance Correction*. This is a lower bound of the true significance.Test of Homo

8、geneity of VariancesE-SFCLevene Statisticdf1df2Sig.2.601335.067（2） 单因素方差分析ANOVAE-SFCSum of SquaresdfMean SquareFSig.Between Groups1978.9443659.64877.789.000Within Groups296.800358.480Total2275.74438Multiple ComparisonsDependent Variable:E-SFC(I) 药物(J) 药物Mean Difference (I-J)Std. ErrorSig.95% Confide

9、nce IntervalLower BoundUpper BoundLSD对照组淫羊霍-20.067*1.338.000-22.78-17.35党参-7.667*1.338.000-10.38-4.95黄芪-8.067*1.338.000-10.78-5.35淫羊霍对照组20.067*1.338.00017.3522.78党参12.400*1.302.0009.7615.04黄芪12.000*1.302.0009.3614.64党参对照组7.667*1.338.0004.9510.38淫羊霍-12.400*1.302.000-15.04-9.76黄芪-.4001.302.761-3.042.2

10、4黄芪对照组8.067*1.338.0005.3510.78淫羊霍-12.000*1.302.000-14.64-9.36党参.4001.302.761-2.243.04Dunnett t (2-sided)a淫羊霍对照组20.067*1.338.00016.7923.34党参对照组7.667*1.338.0004.3910.94黄芪对照组8.067*1.338.0004.7911.34*. The mean difference is significant at the 0.05 level.a. Dunnett t-tests treat one group as a control,

11、and compare all other groups against it.5.随机区组（配伍组）设计资料两因素ANOVA与多重比较 P72L5-3 SPSS操作主要结果Tests of Between-Subjects EffectsDependent Variable:治愈天数SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model43.467a67.24416.718.000Intercept1520.06711520.0673507.846.000年龄24.93346.23314.385.001疗法18.53329

12、.26721.385.001Error3.4678.433Total1567.00015Corrected Total46.93314a. R Squared = .926 (Adjusted R Squared = .871)Pairwise ComparisonsDependent Variable:治愈天数(I) 疗法(J) 疗法Mean Difference (I-J)Std. ErrorSig.a95% Confidence Interval for DifferenceaLower BoundUpper Bound中西结合中医-.600.416.188-1.560.360西医-2.

13、600*.416.000-3.560-1.640中医中西结合.600.416.188-.3601.560西医-2.000*.416.001-2.960-1.040西医中西结合2.600*.416.0001.6403.560中医2.000*.416.0011.0402.960Based on estimated marginal meansa. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).*. The mean difference is sign

14、ificant at the .05 level.6.拉丁方设计资料三因素ANOVA P76L5-4 SPSS操作主要结果Tests of Between-Subjects EffectsDependent Variable:斑块面积SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model1726.562a9191.84014.145.002Intercept.0631.06310773.461.000中药1608.6883536.22939.538.000窝别18.68736.229.459.721饲料99.187333.0

15、622.438.163Error81.375613.563Total.00016Corrected Total1807.93715a. R Squared = .955 (Adjusted R Squared = .887)Pairwise ComparisonsDependent Variable:斑块面积(I) 中药(J) 中药Mean Difference (I-J)Std. ErrorSig.a95% Confidence Interval for DifferenceaLower BoundUpper BoundAB-12.000*2.604.004-18.372-5.628C10.

16、000*2.604.0093.62816.372D-15.250*2.604.001-21.622-8.878BA12.000*2.604.0045.62818.372C22.000*2.604.00015.62828.372D-3.2502.604.259-9.6223.122CA-10.000*2.604.009-16.372-3.628B-22.000*2.604.000-28.372-15.628D-25.250*2.604.000-31.622-18.878DA15.250*2.604.0018.87821.622B3.2502.604.259-3.1229.622C25.250*2

17、.604.00018.87831.622Based on estimated marginal means*. The mean difference is significant at the .05 level.a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).7.2x2析因设计资料的ANOVA P77L5-5 SPSS操作主要结果Tests of Between-Subjects EffectsDependent Variable:胆固醇降

18、低量(mg%)SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model5298.917a31766.30641.077.000Intercept21252.083121252.083494.234.000a药4144.08314144.08396.374.000b药884.0831884.08320.560.002a药 * b药270.7501270.7506.297.036Error344.000843.000Total26895.00012Corrected Total5642.91711a. R Squared = .9

19、39 (Adjusted R Squared = .916)8.2x2交叉设计资料ANOVA P78L5-6 SPSS操作主要结果Tests of Between-Subjects EffectsDependent Variable:巴氏小胃盐酸分泌量(mol/h)SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model1128.000a1386.7694.132.015Intercept8664.00018664.000412.571.000阶段24.000124.0001.143.310狗号1008.0001191.636

20、4.364.014药物96.000196.0004.571.058Error210.0001021.000Total10002.00024Corrected Total1338.00023a. R Squared = .843 (Adjusted R Squared = .639)9.组内分组设计资料两因素ANOVA P79L5-7 SPSS操作主要结果Tests of Between-Subjects EffectsDependent Variable:M物质SourceType I Sum of SquaresdfMean SquareFSig.Corrected Model6.114a4

21、1.52912.778.000Intercept138.5391138.5391158.124.000产地5.85022.92524.452.000部位.2642.1321.104.363Error1.43512.120Total146.08917Corrected Total7.55016a. R Squared = .810 (Adjusted R Squared = .746)Pairwise ComparisonsDependent Variable:M物质(I) 产地(J) 产地Mean Difference (I-J)Std. ErrorSig.a95% Confidence In

22、terval for DifferenceaLower BoundUpper Bound1.327*.210.000.8691.785.306.223.196-.181.792-1.327*.210.000-1.785-.869-1.021*.233.001-1.528-.514-.306.223.196-.792.1811.021*.233.001.5141.528Based on estimated marginal means*. The mean difference is significant at the .05 level.a. Adjustment for multiple

23、comparisons: Least Significant Difference (equivalent to no adjustments).Pairwise ComparisonsDependent Variable:M物质(I) 部位(J) 部位Mean Difference (I-J)Std. ErrorSig.a95% Confidence Interval for DifferenceaLower BoundUpper Bound当归头当归身-.266.180.164-.658.125当归尾-.192.309.546-.865.481当归身当归头.266.180.164-.125

24、.658当归尾.075.298.807-.575.724当归尾当归头.192.309.546-.481.865当归身-.075.298.807-.724.575Based on estimated marginal meansa. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).10.完全随机设计两组协方差分析 P103L6-10 SPSS操作主要结果（1） 用散点图初步判断两比较组是否有直线趋势（2） 用交互项来检验两比较组总体直线回归系数是否相等

25、，结果如下Tests of Between-Subjects EffectsDependent Variable:用药后SourceType I Sum of SquaresdfMean SquareFSig.Corrected Model1389.299a3463.10021.357.000Intercept.2861.28611829.679.000组别326.9041326.90415.076.001用药前1029.54111029.54147.479.000组别 * 用药前32.854132.8541.515.230Error520.4152421.684Total.00028Corr

26、ected Total1909.71427a. R Squared = .727 (Adjusted R Squared = .693)（3）比较修正均数是否相等Tests of Between-Subjects EffectsDependent Variable:用药后SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model1356.445a2678.22330.646.000Intercept14.025114.025.634.433组别251.3201251.32011.356.002用药前1029.54111029.5

27、4146.521.000Error553.2692522.131Total.00028Corrected Total1909.71427a. R Squared = .710 (Adjusted R Squared = .687)11.随机区组（配伍组）设计资料的协方差分析 P104L6-11 SPSS操作主要结果 （1）用散点图初步判断三组的进食量与体重增量是否都有直线趋势（2）用交互项来检验三组总体直线回归系数相等，结果如下Tests of Between-Subjects EffectsDependent Variable:体重增量SourceType I Sum of Squaresd

28、fMean SquareFSig.Corrected Model73210.103a164575.63137.601.000Intercept.5881.5881330.885.000饲料47809.096223904.548196.441.000窝别19137.032111739.73014.297.000进食量6197.42416197.42450.929.000饲料 * 进食量66.550233.275.273.764Error2312.07019121.688Total.76036Corrected Total75522.17235a. R Squared = .969 (Adjust

29、ed R Squared = .944)（3）比较修正均数是否相等Tests of Between-Subjects EffectsDependent Variable:体重增量SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model73143.552a145224.53946.126.000Intercept1708.43611708.43615.083.001饲料478.9122239.4562.114.146窝别3796.27511345.1163.047.014进食量6197.42416197.42454.715.00

30、0Error2378.62021113.268Total.76036Corrected Total75522.17235a. R Squared = .969 (Adjusted R Squared = .948)12.四格表的Pearson 2检验 P121L8-1 SPSS操作主要结果Chi-Square TestsValuedfAsymp. Sig. (2-sided)Exact Sig. (2-sided)Exact Sig. (1-sided)Pearson Chi-Square56.772a1.000.000.000Continuity Correctionb53.6191.000

31、Likelihood Ratio49.4681.000Fishers Exact TestLinear-by-Linear Association56.6211.000N of Valid Cases376a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 8.24.b. Computed only for a 2x2 table注： Pearson Chi-Square 适用条件 n40 且T5 Continuity Correctionb n40 且1T5 Fishers Exact

32、 Test n40 且T113.RxC表2检验与多重比较 P126 L8-4 SPSS操作主要结果Chi-Square TestsValuedfAsymp. Sig. (2-sided)Pearson Chi-Square9.596a6.143Likelihood Ratio9.7416.136Linear-by-Linear Association4.0151.045N of Valid Cases199a. 2 cells (16.7%) have expected count less than 5. The minimum expected count is 3.59.14.方表资料检

33、验（Pearson，McNemar，Kappa） P130L8-9 SPSS操作主要结果Chi-Square TestsValueExact Sig. (2-sided)McNemar Test.454aN of Valid Cases168a. Binomial distribution used.Symmetric MeasuresValueAsymp. Std. ErroraApprox. TbApprox. Sig.Measure of AgreementKappa.809.04510.500.000N of Valid Cases168a. Not assuming the null

34、 hypothesis.b. Using the asymptotic standard error assuming the null hypothesis.15.完全随机设计两组计量资料Wilcoxon秩和检验 P14216.完全随机设计两组等级资料Mann-Whitney U检验 P143L9-3 SPSS操作主要结果Test Statisticsb抑制率Mann-Whitney U15.000Wilcoxon W43.000Z-.857Asymp. Sig. (2-tailed).391Exact Sig. 2*(1-tailed Sig.).445aa. Not corrected

35、for ties.b. Grouping Variable: 葛根剂量17.完全随机设计多组计量资料Kruskal-Wallis H 检验 P144L9-5 SPSS操作主要结果Test Statisticsb死亡率N15Median24.0000Chi-Square10.179adf2Asymp. Sig.006a. 6 cells (100.0%) have expected frequencies less than 5. The minimum expected cell frequency is 2.3.b. Grouping Variable: 药物Test Statisticsa

36、,b死亡率Chi-Square9.740df2Asymp. Sig.008a. Kruskal Wallis Testb. Grouping Variable: 药物18. 两个大样本等级资料Ridit分析 P15219. 多个大样本等级资料Ridit分析L9-11 SPSS操作主要结果（1） 计算标准组（2） 计算标准组疗效各等级R值（3） 计算对比组总体R均值的置信区间DescriptivesStatisticStd. ErrorPROPORTION of 疗效 using RANKITMean.95% Confidence Interval for MeanLower Bound.Upp

37、er Bound.5% Trimmed Mean.Median.Variance.051Std. Deviation.Minimum.3611Maximum.9810Range.6199Interquartile Range.4532Skewness1.119.171Kurtosis-.611.34120.圆形分布资料两角均数的比较 P163L10-5 (1)参数法Watson-William检验(适用于有集中趋势的资料r 0.7)/非参数法Watsons U2检验；（2）正态性检验；（3）两样本平均角比较的t检验。21. 多应变量多组Wilks lambda检验（多元方差分析） P231L1

38、6-3 SPSS操作结果Multivariate TestscEffectValueFHypothesis dfError dfSig.InterceptPillais Trace.987994.174a2.00026.000.000Wilks Lambda.013994.174a2.00026.000.000Hotellings Trace76.475994.174a2.00026.000.000Roys Largest Root76.475994.174a2.00026.000.000贫血类别Pillais Trace.5535.1594.00054.000.001Wilks Lambda

39、.5115.192a4.00052.000.001Hotellings Trace.8345.2094.00050.000.001Roys Largest Root.6388.614b2.00027.000.001a. Exact statisticb. The statistic is an upper bound on F that yields a lower bound on the significance level.c. Design: Intercept + 贫血类别Pairwise ComparisonsDependent Variable(I) 贫血类别(J) 贫血类别Me

40、an Difference (I-J)Std. ErrorSig.a95% Confidence Interval for DifferenceaLower BoundUpper Bound血红蛋白AB-11.033*3.154.002-17.505-4.561C-.3333.362.922-7.2336.566BA11.033*3.154.0024.56117.505C10.700*3.494.0053.53017.870CA.3333.362.922-6.5667.233B-10.700*3.494.005-17.870-3.530红细胞计数AB-.353.180.060-.723.016

41、C-.483*.192.018-.877-.089BA.353.180.060-.016.723C-.130.200.520-.540.280CA.483*.192.018.089.877B.130.200.520-.280.540Based on estimated marginal means*. The mean difference is significant at the .05 level.a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustmen

42、ts).22.重复测量资料的ANOVA P233L16-4 SPSS操作主要结果Multivariate TestsbEffectValueFHypothesis dfError dfSig.factor1Pillais Trace.85420.469a2.0007.000.001Wilks Lambda.14620.469a2.0007.000.001Hotellings Trace5.84820.469a2.0007.000.001Roys Largest Root5.84820.469a2.0007.000.001factor1 * 组别Pillais Trace.4492.857a2.

43、0007.000.124Wilks Lambda.5512.857a2.0007.000.124Hotellings Trace.8162.857a2.0007.000.124Roys Largest Root.8162.857a2.0007.000.124a. Exact statisticb. Design: Intercept + 组别 Within Subjects Design: factor1Mauchlys Test of SphericitybMeasure:MEASURE_1Within Subjects EffectMauchlys WApprox. Chi-Squared

44、fSig.EpsilonaGreenhouse-GeisserHuynh-FeldtLower-boundfactor1.5713.9212.141.700.909.500Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.a. May be used to adjust the degrees of freedom for the averag

45、ed tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.b. Design: Intercept + 组别 Within Subjects Design: factor1Tests of Within-Subjects EffectsMeasure:MEASURE_1SourceType III Sum of SquaresdfMean SquareFSig.factor1Sphericity Assumed190.067295.03334.246

46、.000Greenhouse-Geisser190.0671.400135.78934.246.000Huynh-Feldt190.0671.818104.56634.246.000Lower-bound190.0671.000190.06734.246.000factor1 * 组别Sphericity Assumed24.867212.4334.480.029Greenhouse-Geisser24.8671.40017.7664.480.048Huynh-Feldt24.8671.81813.6804.480.033Lower-bound24.8671.00024.8674.480.067Error(factor1)Sphericity Assumed44.400162.775Greenhouse-Geisser44.40011.1983.965Huynh-Feldt44.40014.5413.053Lower-bound44.4008.0005.55023.多重线性回归 P241L17-1 SPSS操作主要结果Model SummarycModelRR SquareAdjusted R SquareStd. Error