生物统计学A2009答案.doc

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（The most common types of data） 答：Quantitative data, ranked (ordinal) data, and categorical (nominal) data2、为何需要数据转化（Why data transformation） 答：three assumptions for parametric analyses (1) Data from each group were obtained randomly from a normal population; (2) the sampled populations must all have equal variances (in which case it can be said that the variances are homoscedastic); and (3) the effects of the factor levels must be assumed to be additive Data need to be transformed if the aforementioned three assumptions are not met when employing parametric and other related analyses3、如何从总体抽样（How to sample from populations） 答：Randomly sampling - random table and other randomly sampling methodsSize and shape of samples Size and number of samples - when precision is hold constant, there is an inverse relationship between size and number of samplesN = 4s2 / d2 4、双因子方差分析的变异来源（Sources of variation in two-factor analysis of variance） 答：within (error) groups (samples) SS = SS (Xij Xi)2, within groups DF = S (ni 1) = N - k among groups SS = S ni (Xi X)2 = S(S Xij)2 / ni C among group DF = k 1total SS = S S (Xij X)2 = error SS + groups SS = S S Xij 2 C total DF = N 1 = error DF + groups DF C = (S S Xij ) 2 / N5、试述统计分析的重要性（Why statistical analyses important） 答：Many of the investigations in life sciences have become quantitative, in that a great many types of environmental observations consist of numerical facts called data. As life entities are counted or measured, it becomes apparent that some objective methods are necessary to aid the investigator in collecting, presenting, analyzing and reporting research data. Before data can be analyzed, they must be collected, and here statistical considerations can aid in the design of experiments and in the setting up of hypotheses to be tested. Thus, a knowledge of basic statistical principles and procedures is important even before an experiment is begun.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 The following data are recorded as the observed frequencies (O), by which you may use to test whether the sample comes from a population having a 2: 2: 2: 1 color pattern of black to brown to blond to red hair colorations. You are asked: (1) to show the expected frequencies (E), and (2) to decide the trueness of the null hypothesis (H0) using Chi-square goodness of fit (X2-test) and Log-likelihood ratio (G-test). Please note that the critical value is 7.815 when P = 0.05 and df = 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 0.05 2、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 The following data are the length of the menstrual cycle in a random sample of human females. Testing the hypothesis that the mean length of human menstrual cycles is equal to a lunar month (a lunar month is 29.5 days). For a two-tailed test, the critical t value is 2.145 when P = 0.05 and df = 14月经天数数据（Data on the length of the menstrual cycle）：26, 24, 29, 33, 25, 26, 23, 30, 28, 27, 29, 26, 29, 32 and 28 dayst = 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（Using G-test to examine whether the frequency distribution of human hair color in the following 2 4 contingency table is independent of sex. Please note that the critical G value is 7.815 when P = 0.05 and df = 3）发色（Hair color）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-way ANOVA）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 Using the data in the left table to test the null hypothesis that male and female turtles have the same mean serum cholesterol concentrations Serum cholesterol (mg/100 ml) by using Students t-test, Mann-Whitney U-test and one-way ANOVAt = 0.192757, df = 15, P = 0.849735U = 30, U = 42, P = 0.5637F1, 15 = 0.0372, P = 0.8497Teaching assistant ATeaching assistant BGradeRank of gradeGradeRank of gradeA2.5A2.5A2.5A2.5A-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（Using the data in the left table to test the null hypothesis that the academic performance of students is the same under the two teaching assistants by using Mann-Whitney U-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 The appendix is a dataset on the effects of incubation temperature on incubation length and hatchling traits of effects of temperature on incubating eggs and hatchling traits of a hypothetic ectotherm. You are asked to paste this dataset into a statistical package to do the following statistical analyses1、 试用G-检验检测30 C孵出的幼体是否偏离1：1性比 Using G-test to examine if the sex ratio of hatchlings from the incubation temperature of 30 C differs from equality, namely females: males = 1: 1. The critical G value is 3.841 when P = 0.05 and df = 1G = 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（Using two-factor ANOVA with incubation temperature and sex as the factors to examine the effects of incubation temperature, sex and temperature sex interaction on SVL of hatchlings）Temp: F3, 105 = 0.780, P = 0.507Sex: F1, 105 = 2.427, P = 0.122Interaction: F3, 105 = 1.160, P = 0.3293、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 Filling the following table to show descriptive statistics of incubation length for male hatchlings, and then using an appropriate statistical method to examine the differences in incubation length among the four temperature treatments孵化温度Temperature有效样本Valid N平均值Mean标准误Standard error标准差Standard deviation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Using one-factor ANCOVA (with incubation temperature as the factor and initial egg mass as the covariate) to fill the following table, and then to examine whether there are differences in adjusted means of SVL and HWM among the four temperature treatments with the same method变量（variable）平行性（斜率）检验的F值和显著性水平（F value and significance levels for slopes）截距检验的F值和显著性水平（F value and significance levels for intercepts）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 Using one-factor ANCOVA (with incubation temperature as the factor and hatchling SVL as the covariate) to fill the following table, and then examining whether incubation temperature affects head length and head width of hatchlings, and then to examine whether there are differences in adjusted means of HL and HW among the four temperature treatments with the same method变量（variable）平行性（斜率）检验的F值和显著性水平（F value and significance levels for slopes）截距检验的F值和显著性水平（F value and significance levels for intercepts）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-Keuls test: 24b, 26a, 28ab, 30b6、请用主成分分析（特征值 1）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Using a principle component analysis (eigenvalues 1) to examine the existence of variation in morphological phenotypes of hatchlings from the four incubation temperatures. Egg size effect should be removed in all cases using residuals from regressions on IEM (initial egg mass). You are asked to fill the following table; and (2) to show morphological variables that have a main contribution to each resolved factor (vector)变量（variable）负载系数（factor loading）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（variance explained） (%)48.265425.4224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（The effects of incubation temperature on incubation length and hatchlings of a hypothetic ectotherm）Temperature: 孵化温度（Incubation temperature）SEX: 孵出幼体性别（The sex of hatchlings）；1 = female and 2 = maleDINC: 孵化时间（Days of incubation）IEM: 入孵卵重（Initial egg mass）in gramSVL: 幼体体长（Hatchling snout-vent length）HWM: 幼体湿重（Hatchling wet mass）in gramHL: 幼体头长（Hatchling head length）HW: 幼体头宽（ Hatchling head width）Temperature（C）SEXDINCIEMSVLHWMHLHW24157.514.595526.0511.2631515.327.1124157.715.08228.313.773714.97.732415415.806227.212.698914.617.0324156.817.7772916.023315.336.8624157.418.07929.116.027615.646.9624154.118.694528.4514.376815.587.2224157.318.9132615.891714.657.0824156.619.67229.214.830115.337.5224156.219.719527.816.306315.4057.4552415620.91130.315.517915.967.1624155.821.6425.68.985414.786.9524156.521.669529.4517.2889516.0757.5124156.321.912529.9517.511216.017.692415522.210330.416.909415.687.4124256.511.55724.810.96916.227.0624257.413.64225.710.524215.317.0924256.215.59726.712.73815.477.09524258.815.61728.414.249216.077.462425715.766626.212.128414.887.352425716.20728.514.815215.287.3824254.716.36227.613.069115.3357.1824259.816.4912915.359715.787.5624256.916.63327.614.279415.877.524254.116.692526.2512.9264515.077.1652425817.55328.614.990415.787.2424256.917.90728.715.265915.527.3824255.219.45728.0514.500116.317.3824255.924.14328.518.139216.698.1426161.513.83226.811.1165515.397.01526158.514.89328.113.242115.477.4426157.315.32627.412.728815.837.6226158.315.978726.312.175614.777.0526158.915.9826.712.562414.96.9926159.616.06727.713.193515.137.0826157.916.45728.112.377515.137.7726164.416.94828.214.332915.657.3726157.518.59828.414.220615.787.8526160.219.93629.7515.265416.1057.2726159.420.54829.115.230216.487.872616121.34228.717.330915.937.5526159.221.49130.2516.947315.597.6626262.314.712712.038416.377.2426262.714.88327.213.364615.77.0126254.815.433126.311.972414.897.3626258.415.99627.512.758215.757.6626260.516.2353326.512.8785715.606677.50333326259.316.28728.314.278915.447.2626261.319.370529.3516.561316.197.5426257.719.54828.715.317316.227.282626119.6629.516.957716.187.726260.219.950528.9515.7136516.437.59526258.619.99128.515.496116.27.7726260.220.276527.716.634715.887.5926259.520.44528.0516.946816.0857.94526260.221.58529.916.912816.478.226260.523.5511730.417.49916.257.73666728163.314.7726.4513.273715.1857.26528159.715.81727.812.600515.537.4128163.315.92527.514.510115.217.3428160.516.29527.413.618814.946.952816116.35828.214.235115.446.828154.816.920926.812.758515.166.828160.716.950528.814.9574515.3256.83528156.717.481526.2512.4310515.4557.2128158.417.889528.4513.3031515.9357.2728158.820.0229.615.637416.257.662816020.64129.215.522515.717.6428160.320.9429.116.584415.947.428159.421.16929.316.065315.627.072815922.0731529.5517.3117515.827.212826112.5124.89.296814.876.928260.714.52925.3666710.995415.396677.2328256.316.152926.612.318215.387.1128258.116.28527.312.266315.617.4428263.216.70228.314.623315.687.328263.717.0692714.621816.387.