2012统计学A答案

1、杭州师范大学生命与环境科学学院2011-2012学年第一学期期末考试环境统计学试卷（A）参考答案一、基础统计分析1、用下表人类头发颜色观测频次（0）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（G-test）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。BlackBrownBlondRedNO50502020140E40404020140X2= 15.0 7.81 P 7.81 P 0.05 头发颜色不符合 2： 2： 2： 1卡方检验：X2=寸I O -E I-0.52 /气（注意只有在自由度=1的时候，要减去0.

2、5）i=1G检验：O（实际值），E（理论值）=纵和*横和/总和2*O*LN（O/E）求和=G值2、下面是一组随机抽样调查女性月经周期的数据，检测女性平均月经周期等于农历月29.5天） 的假设是否成立。月经周期数据：22, 28, 24, 29, 33, 25, 26, 23, 30, 28, 27, 29, 26, 29, 32 and 27 dayst = -2.80 df = 15 P = 0.0133 0.05 差异显著Statistics-Basic statistics-（t-text dependent）-选样本（左数据，右平均值）-ok-summary（单因子）T-test fo

3、r Dependent S：ajiLples （Spreadsheet 1）Marked differenc已m are miEnificaiit at 口 7.81; df = 3; P 0.05;人类发色频次分布与性别有关。BlackBrownBlondRed1 U LdlMale70902020200Female1101301263440018022014654600.破73.3333333348.WW7通120146.666666797.33333333360E706021.58109518:舛73.3333333336.86299428So48.66666667-35.5704023

4、32018.4.21442062110120-196666667总1.363方蟀126湃.澎游游弗65.051379133436-金 8772141箜.746854924、右表是某两种鸟翼长的抽样数据，试分别用t-检验、Mann-Whitney秩检验和单因子方差分析检测两种鸟的Species ASpecies B翼长是否存在差异31.642.2t = 4.716, df = 16, P = 0.000233 差异显著33.444.034.242.2U = 4 P = 0.00138差异显著35.944.06A B37.242.2T 检验： Statistics-Bas

5、ic statistics-（t-text independent 竖40.044.0的箭头）-选样本-ok-summary40.242.2X-43.444.0MeanMean +-value dfpVarj.able1247.5Vari36. 98750144. 16000 -4. 71649 16 0.00023349.3U 检验：Statistics-Nonparametrics-comparing two independent samples-选样本（左数据，右组别） -M-W U text（2 个因子）Rank Sum Eank Sujtl Group 1 I Group 2UZp

6、-level40. 000005 131. 00004.0000000. 001J815、请填写以下未完成的表格并用Mann-Whitney检验由两个助教指导的学生是否具有相同的学业 表现U = 73; P = 0.101;差异不显著1414181181121115. 5115. 511&. 5118. 5118. 5118; 5121. 5121. 5142424102您1221425252况2以22522922S229|2Teaching assistant ATeaching assistant BGradeRank of gradeGradeRank of gradeA+1A4A4A4

7、A4A4A-8B +10A8B12A-8B12B12B-14C+15.5D25C+15.5D25C18.5D25C18.5D25C18.5D25C18.5D-29C-21.5D-29C-21.5D-29U 检验：Statistics-Nonparametrics-comparing two independent samples-选样本（左数据，右组别）-M-W U text（2 个因子）variableRank SwaGroup 1Rank Sujtl Group 2UEp-levelVari193. 00001i 272.000073.0C000-1.63838G, 1013436.抽测某

8、渔场16次放养记录，结果如表（x1:投饵量，x2:放养量y：鱼产量。单位: kg）。试求：x19.58.013.59.512.59.412.58.06.512.9x21.92.03.21.9y7.16.410.410.97.010.07.99.312.87.57.77.09.5鱼产量对投饵量、放养量的线性回归方程。y = 0.584x1+2.964x2-4.349复相关系数和x1、x2的偏相关系数。0.823x1: 0.655x2： 0.819线性回归方程:Stat

9、istics-Multiple Regression-选样本(左 y 右 x)-ok-summaryRegression Sumnary for Dependent Variable: y (Spreadsheet 1. sti) R= .82285858 R2- .67709625 Adjusted R2= .62741875 FW3) = 13. ESCI p.W 口口口64 Std. Errnr nf 契1. 1312N=16BetaSt d. Err.of BetaBSt d. Err.of Bt (13)：p-levelInterceptxlx20.8193480. 171478-4

10、.34S530.58415F 96376.2.-55S10. 153C0. 6202136-1-.53 84?79985 1泗 78160.1129450. 0003611结果：线性回归方程。y = 0.584x1+2.964x2-4.349复相关系数和x1、x2的偏相关系数：0.823x1: 0.655 x2： 0.819二、综合统计分析附录是孵化温度对某种卵生变温动物卵孵化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1、试用G-检验检测28 C孵出的幼体性比是否偏离1： 1G = 0.291 0.05;未偏离 1: 1 性比2、试用以孵化热环境和性别为

11、因子的双因子方差分析分别显示不同孵化热环境温度、不同性别，以及孵化热环境与性别的交互作用对孵化时间（DINC）的影响temp: F3 116= 23.7; P 0.001sex: F1 116= 0.1; P = 0.728temp*sex: F3 116= 5.0; P = 0.00261Statistics-ANOVA-Factorial AMOVA-选样本（左 DINC 右 SEX,TEMP）-OK- All effectsEffectSSDegr. ofFreedomMSFPIntercept409336. 211409336. 2123149. 10.000000IBM236. 23

12、78. 723. 70.000000SEX0.410.40. 10. 72f833TEM*SEX50. 1316. 75. 00.002607Error85. 6116is. 33、填充下表，随后用恰当的统计方法比较四个温度处理下的入孵卵重的平均值是否 存在差异TemperatureValid NMeanMedianRangeStandard deviationStandarderror24 C3117.817.612.63.280.5926 C3118.310.4928 C3118.317.510.52.880.5230 C32.450.44F3

13、120= 177； P = 0.912Statistics-Basic Statistics-Descriptive Statistics选样本(lEM)-select cases (Tem=24)-OK-SummaryVariableValid NMe anMe di ：ai_iR：di_LgeSt d. Dev.St ：diidar d ErrorIEM3117. 8：357517.5530012;586000.589907Statistics-ANOVA-one way-选样本(左 IEM 右 TEM)-ok-All effectsEffectssDegr. ofFreedomMSFPI

14、nt ercept40816. 311140816. 315028. 7100. 000000TEM4. 3131.440. 1770. 911695Error974.00迦4、请以初生卵重为协变量、孵化热环境为因子的单因子协方差分析填充以下表格， 并检验孵化温度是否显著影响表中两个幼体变量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)SVLF3116= 2.056; P =

15、0.110F3, 119= 1.341; P = 0.264HWMF3,116=顷 P = O.153F3 119= 0.757; P = 0.520Effect- - - - - - - - - - - -SSDegr. of FreeduiiLMSFpIntercept1320. 342111320. 3421384.5330.ooooocTEM6. 206-.32.0692.-1690.09539S丘M105. 237110&. 237110. 3550.OOOOOCTEM*IEFu15. 88231. 9612.-0560. 109895Error110. 6221160. 9545、

16、请以幼体体长SVL为协变量、孵化热环境为因子的单因子协方差分析填充以下表 格，并检验孵化温度是否显著影响表中两个幼体变量，并检验矫正后的头长HL和头 宽HW在四个温度下的差异（用Tukeys post腐重比较）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)HLF3116= 0.943; P = 0.423F3,119= 1.432; P = 0.237HWF3116= 1.02

17、4; P = 0.385F3119= 149.84; P b c)平仃性：Statistics-Advanced linear-General Linear-Homogeneity of slops-ok选样本(左：HL 中：单因子 Tem 右：协变量 SVL)-OK-All effectsEffectUnivariate Tests of Signific：ai_ice for HL (Spreadsheets) Sigma-r巳stricted par：ajrLet erizationEffect ive hyp ot he sis dec cimposit i onssDegr. ofF

18、reedoiTLMSFPIntercept33. 812111. 133.81211216.06940.000000TEM0.5932430. 1J1080. 83760.475877SVL环境统计学试单而氏参考兔己案及评分标准（塑R市共11舌TEM* SUL0.44 240. 147480?9425七：迪白如Error18.152521160. 15649截距检验：Statistics-Advanced linear-General Linear-Analysis of covariance-选样本(左：HL 中：单 因子 Tem 右：协变量 SVL)-OK-All effectsUniva

19、riate Tests of Significance for HL (Spreadsheet3 Sigma-restricted parameterizationEffective hypcitheEig deccimp矣ititmEffectSSDegr. of FreedomMSFPIntercept38. 2232311138. 22323244.61250. 000000SVL5. 749305. 7493036.79310. 000000TEM0.6713730:223791.432S0/236852Iirrcr18. 59498119|F 15626p黑色，无差异。共同斜率：St

20、atistics-Advanced linear-General Linear-Analysis of covariance-选样本(左：HW 中: 单因子 Tem 右： 协变量 SVL)-OK-more result-summart-coeficientiffectParameter Estimates(平行线， Sigma-restricted paranteteri:Level of EffectColUJlLfLHW_ Param.Interceptii|4.658078SVL20.087217K=0.087217TEM：2430.211664TEM2640.387370r匚爵0(?R

21、nY=y-k(x-平均值)H共同斜率*k ：（协变量VL）v校正后的朝芸0.08721729.457.51r6. 6S579.$3&0.08721729.957.696. Sl.90850 08721730.47.41E知9液将校正后的的HW复制到SATISTICA，Statistics-ANOVA-one way-选样本(左 HW右 TEM)-ok-more result-Post hoc-Tukey HsdTuk豉:HSD test; variable cor hw (平行线，截距. Approximate Probabilities for Post Hoc Tests Errnr： E

22、imtween ,= .口&1口、df = 12CL WCell No.TEM7.31187.487537. 30994 fi.2914140. 0301170.9999920.0001362H0. 0301170. 0277640.000136a280. 99999歹0.0277640.00013640. 0001360. 0001360. 00013626 a(1)24 b28 b30 c6、请用主成分分析（特征值 0.5）检测从四个温度孵出的幼体是否存在形态表型变 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（1）填写下表（2）显示各区分出的向量中起主要作用的形态变量

23、variablefactor loadingFactor (PC) 1Factor (PC) 2Factor (PC) 3SVL0.822527-0.232534-0.242172HWM0.839207-0.163942-0.217526HL0.5780060.2890500.762791HW0.1750070.924389-0.338017variance explained (%)43.638425.474820.0518l.Statisticas-Multiple Regession-选变量(SVL/HWM/HL/HW,IEM-OK-continue-continue-OK-OK-sum

24、mary Residuals将四个变量的Residuals复制到excel，取最后四行，求的每列绝对值的最大值，复制，计算: 变量/绝对值的最大值，将计算好的复制到Statistics。2.Statistics -Multivariate Exploratory Techniques-Factor analysis -max写 4， min 按题目特征值写0.5-OK-summary： Factory loadingsFactor Loadings (Unrotated) Spreadsheet 1. st a) Estract ion; Principal componentsVariabl

25、eFactor1FactorFactor3Var90. 822152:1-0. 232535-Ol24172VarlO0. 8392070. 163944-0.217524NewVar10.5780070.2890530.762789NewVar0.1750080.924387-0. B8021Ezpl. Var1.7455381.0189940.802069Prp.To+10.4363840.2547490.200517Appendix: The effects of incubation temperature on incubation length and hatchlings of

26、a hypothetic ectothermTemperature 孵化温度:Incubation temperatureSEX 孵出幼体性别：The sex of hatchlings; 1 = female and 2 = maleDINC 孵化时间：Days of incubationIEM 入孵卵重：Initial egg mass in gramSVL 幼体体长:Hatchling snout-vent lengthHWM 幼体湿重:Hatchling wet mass in gramHL 幼体头长:Hatchling head lengthHW 幼体头宽:Hatchling hea

27、d widthTemperature( C)SEXDINCIEMSVLHWMHLHW24156.521.669529.4517.2889516.0757.5124156.321.912529.9517.511216.017.692415522.210330.416.909415.687.4124157.715.08228.313.773714.97.732415415.806227.212.698914.617.0324156.817.7772916.023315.336.8624157.418.07929.116.027615.646.9624154.118.694528.4514.3768

28、15.587.2224157.318.9132615.891714.657.082415620.91130.315.517915.967.1624155.821.6425.68.985414.786.9524156.521.669529.4517.2889516.0757.5124156.321.912529.9517.511216.017.692415522.210330.416.909415.687.4124256.511.55724.810.96916.227.0624257.413.64225.710.524215.317.0924256.215.59726.712.73815.477

29、.09524256.511.55724.810.96916.227.0624257.413.64225.710.524215.317.0924256.215.59726.712.73815.477.09524258.815.61728.414.249216.077.462425715.766626.212.128414.887.352425716.20728.514.815215.287.3824254.716.36227.613.069115.3357.1824259.816.4912915.359715.787.5624256.916.63327.614.279415.877.524254

30、.116.692526.2512.9264515.077.1652425817.55328.614.990415.787.2424256.917.90728.715.265915.527.3824255.219.45728.0514.500116.317.3824255.924.14328.518.139216.698.1426158.514.89328.113.242115.477.4426157.315.32627.412.728815.837.6226158.315.978726.312.175614.777.0526158.915.9826.712.562414.96.9926164.

31、416.94828.214.332915.657.3726157.518.59828.414.220615.787.8526160.219.93629.7515.265416.1057.2726159.420.54829.115.230216.487.872616121.34228.717.330915.937.5526159.221.49130.2516.947315.597.6626159.420.54829.115.230216.487.872616121.34228.717.330915.937.5526159.221.49130.2516.947315.597.6626262.314

32、.712712.038416.377.2426262.714.88327.213.364615.77.0126254.815.433126.311.972414.897.3626262.314.712712.038416.377.2426262.714.88327.213.364615.77.0126254.815.433126.311.972414.897.3626258.415.99627.512.758215.757.6626260.516.2353326.512.8785715.606677.50333326259.316.28728.314.278915.447.2626261.31

33、9.370529.3516.561316.197.5426257.719.54828.715.317316.227.282626119.6629.516.957716.187.726260.219.950528.9515.7136516.437.59526258.619.99128.515.496116.27.7726260.220.276527.716.634715.887.5926259.520.44528.0516.946816.0857.94526260.221.58529.916.912816.478.226260.523.5511730.417.49916.257.73666728

34、159.715.81727.812.600515.537.4128163.315.92527.514.510115.217.3428154.816.920926.812.758515.166.828160.716.950528.814.9574515.3256.83528156.717.481526.2512.4310515.4557.2128158.417.889528.4513.3031515.9357.2728158.820.0229.615.637416.257.662816020.64129.215.522515.717.6428160.320.9429.116.584415.947

35、.428159.421.16929.316.065315.627.072815922.0731529.5517.3117515.827.2128160.320.9429.116.584415.947.428159.421.16929.316.065315.627.072815922.0731529.5517.3117515.827.212826112.5124.89.296814.876.928260.714.52925.3666710.995415.396677.2328256.316.152926.612.318215.387.112826112.5124.89.296814.876.928260.714.52925.3666710.995415.396677.2328256.316.152926.612.318215.387.1128258.116.28527.312.266315.617.4428263.216.70228.314.623315.687.328263.717.0692714.621816.387.1428261.0117.14127.814.613315.676.8828260.517.28327.514.328515.577.2928260.419.68927.415.51515.797.6628259.319.87728.714.90