生物统计学(a)2009答案解析 9页

专业：学号：姓名：装订线南京师范大学生命科学学院2008-2009学年第一学期硕士研究生期末考试《生物统计学》试卷（A）题号一二三四五六总分得分得分一、简答题（每小题4分，共20分）1、最常见的数据类型（Themostcommontypesofdata）答：Quantitativedata,ranked(ordinal)data,andcategorical(nominal)data2、为何需要数据转化（Whydatatransformation）答：threeassumptionsforparametricanalyses(1)Datafromeachgroupwereobtainedrandomlyfromanormalpopulation;(2)thesampledpopulationsmustallhaveequalvariances(inwhichcaseitcanbesaidthatthevariancesarehomoscedastic);and(3)theeffectsofthefactorlevelsmustbeassumedtobeadditiveDataneedtobetransformediftheaforementionedthreeassumptionsarenotmetwhenemployingparametricandotherrelatedanalyses3、如何从总体抽样（Howtosamplefrompopulations）答：Randomlysampling-randomtableandotherrandomlysamplingmethodsSizeandshapeofsamplesSizeandnumberofsamples-whenprecisionisholdconstant,thereisaninverserelationshipbetweensizeandnumberofsamplesN=4s2/d24、双因子方差分析的变异来源（Sourcesofvariationintwo-factoranalysisofvariance）答：within(error)groups(samples)SS=S[S(Xij–Xi)2],withingroupsDF=S(ni–1)=N-kamonggroupsSS=Sni(Xi–X)2]=S[(SXij)2/ni]–CamonggroupDF=k–1totalSS=SS(Xij–X)2=errorSS+groupsSS=SSXij2–CtotalDF=N–1=errorDF+groupsDFC=(SSXij)2/N5、试述统计分析的重要性（Whystatisticalanalysesimportant）答：Manyoftheinvestigationsinlifescienceshavebecomequantitative,inthatagreatmanytypesofenvironmentalobservationsconsistofnumericalfactscalleddata.Aslifeentitiesarecountedormeasured,itbecomesapparentthatsomeobjectivemethodsare\nnecessarytoaidtheinvestigatorincollecting,presenting,analyzingandreportingresearchdata.Beforedatacanbeanalyzed,theymustbecollected,andherestatisticalconsiderationscanaidinthedesignofexperimentsandinthesettingupofhypothesestobetested.Thus,aknowledgeofbasicstatisticalprinciplesandproceduresisimportantevenbeforeanexperimentisbegun.得分二、基础统计分析（1-2每小题5分，3-5每小题10分，共40分）1、用下表人类头发颜色观测频次（O）的抽样数据，要求：（1）填写头发颜色的理论频次分布；（2）用卡方好适度检测和对数似然比例检测人类黑色、棕色、金色和红色头发颜色是否吻合2：2：2：1的颜色分布。显著性水平为0.05、自由度为3条件下的X2临界值是7.815[Thefollowingdataarerecordedastheobservedfrequencies(O),bywhichyoumayusetotestwhetherthesamplecomesfromapopulationhavinga2:2:2:1colorpatternofblacktobrowntoblondtoredhaircolorations.Youareasked:(1)toshowtheexpectedfrequencies(E),and(2)todecidethetruenessofthenullhypothesis(H0)usingChi-squaregoodnessoffit(X2-test)andLog-likelihoodratio(G-test).Pleasenotethatthecriticalvalueis7.815whenP=0.05anddf=3]黑色（Black）棕色（Brown）金色（Blond）红色（Red）NO46382719130E37373719130X2=4.9189189189,df=3,P>0.05G=5.0429707734,df=3,P>0.052、下列数据是人类女性随机抽样样本中显示的月经周期时间。检测人类月经周期平均时间是否与农历全月天数相同[Thefollowingdataarethelengthofthemenstrualcycleinarandomsampleofhumanfemales.Testingthehypothesisthatthemeanlengthofhumanmenstrualcyclesisequaltoalunarmonth(alunarmonthis29.5days).Foratwo-tailedtest,thecriticaltvalueis2.145whenP=0.05anddf=14]月经天数数据（Dataonthelengthofthemenstrualcycle）：26,24,29,33,25,26,23,30,28,27,29,26,29,32and28dayst=2.54083,df=14,P<0.0235323、用G-检验检测以下2´4联表中人类的发色频次分布是否与性别无关。显著性水平为0.05、自由度为3条件下的G临界值是7.815（UsingG-testtoexaminewhether\nthefrequencydistributionofhumanhaircolorinthefollowing2´4contingencytableisindependentofsex.PleasenotethatthecriticalGvalueis7.815whenP=0.05anddf=3）发色（Haircolor）总数（Total）黑色（Black）棕色（Brown）金色（Blond）红色（Red）男性（Male）64863218200女性（Female）11013012832400G=19.024297914,df=3,P<0.05MalesFemales220.1223.4218.6221.5229.6230.2228.8224.3220.0223.8224.1230.8226.5200.2217.9229.0219.34、左表是某种龟雌雄个体血清中甾醇类激素含量的抽样数据，试分别用t-检验、Mann-Whitney秩检验和单因子方差分析（one-wayANOVA）检测该种龟雌雄个体血清中具有相同甾醇类激素含量的无效假设[Usingthedatainthelefttabletotestthenullhypothesisthatmaleandfemaleturtleshavethesamemeanserumcholesterolconcentrations[Serumcholesterol(mg/100ml)]byusingStudent’st-test,Mann-WhitneyU-testandone-wayANOVA]t=0.192757,df=15,P=0.849735U=30,U'=42,P=0.5637F1,15=0.0372,P=0.8497\nTeachingassistantATeachingassistantBGradeRankofgradeGradeRankofgradeA2.5A2.5A2.5A2.5A-5.5B+7.5A-5.5B+7.5B10B10B10B-12C+13.5C16.5C+13.5C16.5C16.5C-19.5C16.5D23C-19.5D23D23D23D-26.5D23D-26.55、左表是两名助教辅导学生的成绩。试用Mann-Whitney秩检验检测两名助教辅导的学生具有相同学业表现的无效假设（UsingthedatainthelefttabletotestthenullhypothesisthattheacademicperformanceofstudentsisthesameunderthetwoteachingassistantsbyusingMann-WhitneyU-test）U=74,U'=108,P=0.409得分三、综合统计分析（1-4每小题5分，5-6每小题10分，共40分）附录是关于孵化温度对某种变温动物卵孵化期和孵出幼体特征的影响的数据。要求将该组数据粘贴到统计软件包，以便于做以下统计分析[Theappendixisadatasetontheeffectsofincubationtemperatureonincubationlengthandhatchlingtraitsofeffectsoftemperatureonincubatingeggsandhatchlingtraitsofahypotheticectotherm.Youareaskedtopastethisdatasetintoastatisticalpackagetodothefollowingstatisticalanalyses]1、试用G-检验检测30°C孵出的幼体是否偏离1：1性比[UsingG-testtoexamineifthesexratioofhatchlingsfromtheincubationtemperatureof30°Cdiffersfromequality,namelyfemales:males=1:1.ThecriticalGvalueis3.841whenP=0.05anddf=1]G=6.0403853845,df=1,P<0.052、试用以孵化温度和性别为因子的双因子方差分析分别显示不同孵化温度、不同性别、以及孵化温度与性别的交互作用对孵出幼体体长（SVL）的影响（Usingtwo-factorANOVAwithincubationtemperatureandsexasthefactorstoexaminetheeffectsofincubationtemperature,sexandtemperature´sexinteractiononSVLofhatchlings）Temp:F3,105=0.780,P=0.507Sex:F1,105=2.427,P=0.122Interaction:F3,105=1.160,P=0.329\n3、填充下表显示四个温度处理下雄性孵出幼体孵化期的描述性统计值，随后用恰当的统计方法检验四个温度下的孵化期平均值是否存在差异[Fillingthefollowingtabletoshowdescriptivestatisticsofincubationlengthformalehatchlings,andthenusinganappropriatestatisticalmethodtoexaminethedifferencesinincubationlengthamongthefourtemperaturetreatments]孵化温度Temperature有效样本ValidN平均值Mean标准误Standarderror标准差Standarddeviation中值Median范围Range24°C1456.7430.4091.52956.95.726°C1559.8130.5021.94560.27.928°C1460.3940.5061.89460.67.430°C2156.9760.2961.35856.95.7F3,60=19.947,P<0.000124b,26a,28a,30b4、试用以入孵卵重为协变量、孵化温度为因子的单因子协方差分析填充以下表格，随后用该方法检验孵化温度是否影响孵出幼体的体长和体重，如有影响请用任一多重比较方法（要求注明）比较SVL和HWM矫正平均值的温度处理间差异[Usingone-factorANCOVA(withincubationtemperatureasthefactorandinitialeggmassasthecovariate)tofillthefollowingtable,andthentoexaminewhethertherearedifferencesinadjustedmeansofSVLandHWMamongthefourtemperaturetreatmentswiththesamemethod]变量（variable）平行性（斜率）检验的F值和显著性水平（Fvalueandsignificancelevelsforslopes）截距检验的F值和显著性水平（Fvalueandsignificancelevelsforintercepts）幼体体长（SVL）F3,105=0.585,P=0.626F3,108=1.419,P=0.241幼体体重（HWM）F3,105=1.318,P=0.273F3,108=0.246,P=0.8645、试用以幼体体长（SVL）为协变量、孵化温度为因子的单因子协方差分析填充以下表格，随后用该方法检验孵化温度是否影响孵出幼体的头长和头宽，如有影响请用任一多重比较方法（要求注明）比较HL和HW矫正平均值的温度处理间差异[Usingone-factorANCOVA(withincubationtemperatureasthefactorandhatchlingSVLasthecovariate)tofillthefollowingtable,andthenexaminingwhetherincubationtemperatureaffectsheadlengthandheadwidthofhatchlings,andthentoexaminewhethertherearedifferencesinadjustedmeansofHLandHWamongthefourtemperature\ntreatmentswiththesamemethod]变量（variable）平行性（斜率）检验的F值和显著性水平（Fvalueandsignificancelevelsforslopes）截距检验的F值和显著性水平（Fvalueandsignificancelevelsforintercepts）幼体头长（HL）F3,105=0.895,P=0.446F3,108=1.635,P=0.185幼体头宽（HW）F3,105=0.689,P=0.561F3,108=2.769,P<0.05HW:Newman-Keulstest:24b,26a,28ab,30b6、请用主成分分析（特征值³1）检测从四个温度孵出的幼体是否存在大小和形态变异。各处理卵大小效应用入孵卵重与各有关变量的回归剩余值去除。要求填写下表并显示各区分出的向量中起主要作用的形态变量[Usingaprinciplecomponentanalysis(eigenvalues³1)toexaminetheexistenceofvariationinmorphologicalphenotypesofhatchlingsfromthefourincubationtemperatures.EggsizeeffectshouldberemovedinallcasesusingresidualsfromregressionsonIEM(initialeggmass).Youareaskedtofillthefollowingtable;and(2)toshowmorphologicalvariablesthathaveamaincontributiontoeachresolvedfactor(vector)]变量（variable）负载系数（factorloading）Factor(PC)1Factor(PC)2Factor(PC)3幼体体长（SVL）-0.7573160.448402幼体湿重（HWM）-0.7647190.416215幼体头长（HL）-0.689918-0.41011幼体头宽（HW）-0.544342-0.688771解释方差百分比（varianceexplained）(%)48.265425.4224\n附录（Appendix）：孵化温度对某种卵生变温动物孵化期和孵出幼体的影响（Theeffectsofincubationtemperatureonincubationlengthandhatchlingsofahypotheticectotherm）Temperature:孵化温度（Incubationtemperature）SEX:孵出幼体性别（Thesexofhatchlings）；1=femaleand2=maleDINC:孵化时间（Daysofincubation）IEM:入孵卵重（Initialeggmass）ingramSVL:幼体体长（Hatchlingsnout-ventlength）HWM:幼体湿重（Hatchlingwetmass）ingramHL:幼体头长（Hatchlingheadlength）HW:幼体头宽（Hatchlingheadwidth）Temperature（°C）SEXDINCIEMSVLHWMHLHW24157.514.595526.0511.2631515.327.1124157.715.08228.313.773714.97.732415415.806227.212.698914.617.0324156.817.7772916.023315.336.8624157.418.07929.116.027615.646.9624154.118.694528.4514.376815.587.2224157.318.9132615.891714.657.0824156.619.67229.214.830115.337.5224156.219.719527.816.306315.4057.4552415620.91130.315.517915.967.1624155.821.6425.68.985414.786.9524156.521.669529.4517.2889516.0757.5124156.321.912529.9517.511216.017.692415522.210330.416.909415.687.4124256.511.55724.810.96916.227.0624257.413.64225.710.524215.317.0924256.215.59726.712.73815.477.09524258.815.61728.414.249216.077.462425715.766626.212.128414.887.352425716.20728.514.815215.287.3824254.716.36227.613.069115.3357.1824259.816.4912915.359715.787.5624256.916.63327.614.279415.877.524254.116.692526.2512.9264515.077.1652425817.55328.614.990415.787.2424256.917.90728.715.265915.527.3824255.219.45728.0514.500116.317.3824255.924.14328.518.139216.698.1426161.513.83226.811.1165515.397.01526158.514.89328.113.242115.477.4426157.315.32627.412.728815.837.6226158.315.978726.312.175614.777.0526158.915.9826.712.562414.96.99\n26159.616.06727.713.193515.137.0826157.916.45728.112.377515.137.7726164.416.94828.214.332915.657.3726157.518.59828.414.220615.787.8526160.219.93629.7515.265416.1057.2726159.420.54829.115.230216.487.872616121.34228.717.330915.937.5526159.221.49130.2516.947315.597.6626262.314.712712.038416.377.2426262.714.88327.213.364615.77.0126254.815.433126.311.972414.897.3626258.415.99627.512.758215.757.6626260.516.2353326.512.8785715.606677.50333326259.316.28728.314.278915.447.2626261.319.370529.3516.561316.197.5426257.719.54828.715.317316.227.282626119.6629.516.957716.187.726260.219.950528.9515.7136516.437.59526258.619.99128.515.496116.27.7726260.220.276527.716.634715.887.5926259.520.44528.0516.946816.0857.94526260.221.58529.916.912816.478.226260.523.5511730.417.49916.257.73666728163.314.7726.4513.273715.1857.26528159.715.81727.812.600515.537.4128163.315.92527.514.510115.217.3428160.516.29527.413.618814.946.952816116.35828.214.235115.446.828154.816.920926.812.758515.166.828160.716.950528.814.9574515.3256.83528156.717.481526.2512.4310515.4557.2128158.417.889528.4513.3031515.9357.2728158.820.0229.615.637416.257.662816020.64129.215.522515.717.6428160.320.9429.116.584415.947.428159.421.16929.316.065315.627.072815922.0731529.5517.3117515.827.212826112.5124.89.296814.876.928260.714.52925.3666710.995415.396677.2328256.316.152926.612.318215.387.1128258.116.28527.312.266315.617.4428263.216.70228.314.623315.687.328263.717.0692714.621816.387.1428261.0117.14127.814.613315.676.88\n28260.517.28327.514.328515.577.2928260.419.68927.415.51515.797.6628259.319.87728.714.9063515.867.8628261.120.74927.814.554415.67.3928260.520.89627.1516.665815.3857.452826121.639528.917.5428516.027.63528258.723.01828.216.9531516.4257.8530159.712.81652610.4024515.117.10530159.313.15526.7510.235915.1956.9830159.715.784527.8514.0640515.497.2930153.215.902527.111.973915.76.683016116.20627.614.532515.516.9930156.616.25128.212.781215.387.0330160.117.01729.115.384315.777.3230161.217.05228.914.9715.4857.1730256.717.28626.613.215.116.7230257.519.121529.414.6217515.7557.37530255.419.271528.5514.774816.317.25530256.619.42627.616.487615.497.2230256.320.21228.314.946716.167.6330257.620.965530.117.0851516.1857.4130258.521.68929.216.484615.647.4430259.314.775527.313.42315.677.2630254.815.361725.411.688215.467.1130254.915.50926.6512.4754515.377.4730255.916.05427.5513.219715.4657.230260.516.5725.511.780715.117.0930257.516.86122813.8470515.4757.2730257.617.223125.7512.551915.0057.30530256.819.470528.514.5357516.0657.3530255.919.91928.715.350116.147.6130257.220.4927.316.380115.967.30530256.221.22425.315.891815.787.533025721.35528.616.744516.047.8330256.922.01828.215.514116.347.6130257.422.323628.917.1069516.857.57