高級(jí)生物統(tǒng)計(jì)

1、高級(jí)生物統(tǒng)計(jì)試題1、論述試驗(yàn)數(shù)據(jù)為什么要進(jìn)行統(tǒng)計(jì)分析？（結(jié)合實(shí)際例子）20%答：（1）在試驗(yàn)研究中，通過觀察、測(cè)量和記載，可獲得大量的數(shù)據(jù)資料。但這些資料往往是零亂的、無(wú)規(guī)律可循，只有通過對(duì)試驗(yàn)數(shù)據(jù)的整理，才能發(fā)現(xiàn)其內(nèi)部聯(lián)系和規(guī)律性。（2）試驗(yàn)普遍存在試驗(yàn)誤差，用生物統(tǒng)計(jì)方法來(lái)分析試驗(yàn)資料，降低試驗(yàn)誤差，提高試驗(yàn)的精確性，以正確估計(jì)誤差，得到可靠的試驗(yàn)結(jié)論。（3）統(tǒng)計(jì)分析 解決“試驗(yàn)結(jié)果怎么看”的問題。能夠?qū)υ囼?yàn)數(shù)據(jù)用統(tǒng)計(jì)分析方法正確地估計(jì)出試驗(yàn)誤差和處理效應(yīng)，達(dá)到試驗(yàn)的預(yù)期目的。 例如，達(dá)爾文應(yīng)用統(tǒng)計(jì)學(xué)方法研究了生物的連續(xù)變異現(xiàn)象；孟德爾應(yīng)用分組統(tǒng)計(jì)方法發(fā)現(xiàn)了遺傳學(xué)中的分離定律和獨(dú)立分配定律

2、；Karl Pearson用統(tǒng)計(jì)方法研究進(jìn)化問題；Galton用回歸分析方法研究了親子身高的遺傳規(guī)律。 到了20世紀(jì)初，R. A. Fisher提出了方差分析方法，建立了試驗(yàn)設(shè)計(jì)三大原理，并提出了隨機(jī)區(qū)組和拉丁方等試驗(yàn)設(shè)計(jì)方案，出版了經(jīng)典的“Statistical Methods for Research Workers”一書，奠定了生物統(tǒng)計(jì)學(xué)的基礎(chǔ)。 A. Wall，Gosset（筆名student），J. Wishart，T. W. Anderson，Yates，J. Newman和E. Pearson等人都在樣本分布和統(tǒng)計(jì)推斷理論的建立上做出了重要貢獻(xiàn)，推動(dòng)了數(shù)理統(tǒng)計(jì)學(xué)的發(fā)展，同時(shí)也推動(dòng)

3、了生物統(tǒng)計(jì)學(xué)的發(fā)展。 2、試驗(yàn)有兩種不同的飼料添加劑和對(duì)照三處理，重復(fù)9次，有27頭豬參與試驗(yàn)，兩個(gè)月增重資料如下。各個(gè)處理供試豬初始體重見表，試對(duì)資料進(jìn)行分析。解釋說(shuō)明結(jié)果。20%飼料添加劑對(duì)豬增重試驗(yàn)結(jié)果表 (單位：kg)處 理2號(hào)添加劑1號(hào)添加劑對(duì)照觀測(cè)指標(biāo)初重x增重y初重x增重y初重x增重y觀測(cè)值30.535.527.529.528.526.524.525.021.519.522.518.523.021.520.018.532.028.520.520.522.524.519.018.021.025.524.527.516.516.028.531.526.028.535.030.522.

4、522.518.519.022.520.518.520.528.531.515.516.021.524.520.518.517.016.0解答：1、由上表數(shù)據(jù)可得，（1）試驗(yàn)資料的數(shù)學(xué)模型eij+be+ti+my(xij-mx)=yij觀測(cè)值不僅具有飼料效應(yīng)和隨機(jī)誤差，而且還受到初重的影響。故單因素完全隨機(jī)設(shè)計(jì)試驗(yàn)資料觀測(cè)值的數(shù)據(jù)結(jié)構(gòu)式為:(i=1,2,L,k;j=1,2,L,n)（2）計(jì)算回歸系數(shù)并進(jìn)行顯著性檢驗(yàn) be=SPSS=0.9832回歸系數(shù)由誤差項(xiàng)的統(tǒng)計(jì)數(shù)計(jì)算：由DPS軟件計(jì)算回歸方程系數(shù)B結(jié)果如下： 總回歸:回歸截距a=0.4703；回歸系數(shù)b1=0.9893；R=0.88466

5、； 共同回歸: 回歸截距，y1,1=2.2260；y2,1=1.2241；y3,1=-1.6111；回歸系數(shù)b1=0.9832；R=0.92710be=0.9832表示供試豬只初始體重改變1kg，每只豬增重將平均改變0.9832kg。 (3)對(duì)矯正后的每只豬增重作方差分析 1、 求矯正后的每只豬增重的各項(xiàng)平方和及自由度正每只豬增重的總平方和與自由度，即總離回歸平方和與自由度，記為SST、dfT： SST= SSTY SSRY = 170.0957dfY= dfTY- dfRY=22矯正每只豬增重的誤差平方和與自由度，即誤差離回歸平方和與自由度，記為SSe、dfeSSe=SSer=98.8238

6、Dfe= dfer =23矯正每只豬增重處理間平方和與自由度，記為SSt、dftSSe=SST-SSe= 170.0957-98.8238=71.2719Dfe= dfT-dfe=k-1=3-1=22、對(duì)矯正每只豬增重進(jìn)行方差分析 （1）矯正每只豬增重的方差分析表變異來(lái)源dfSSMSF值共同回歸系數(shù)2398.82384.2967回歸截距間271.271935.63608.2938*總 回 歸25 170.0957F=45.6354F0.01(2,20)，p0.01，不同肥料的矯正單株產(chǎn)量間存在極顯著的差異.（2）變量x和y的各項(xiàng)自由度、平方和與乘積和因子間協(xié)方差分析結(jié)果方 差 來(lái) 源平方和自由

7、度均方F值誤 差39.9147152.661013.3876*處理A+ 誤差111.162617處理A 間71.2480235.6240* SIG. 5% * SIG. 1%（3）回歸誤差項(xiàng)方差分析方差來(lái)源平方和自由度均方F值回 歸273.36311273.3631102.7303*離回歸39.9147152.6610總 的313.277816* SIG. 5%, * SIG. 1% (4) 求矯正后的每頭豬增重的各項(xiàng)平方和及自由度調(diào)整各個(gè)處理平均(因子)處 理 平均值 調(diào)整后均值 A1B1 25.222225.1130A2B1 24.111124.1111A3B1 21.166721.275

8、8T-測(cè)驗(yàn) T-測(cè)驗(yàn)結(jié)果(因子) T(y1-y2)= 1.3028NO SIG. SD = 0.7691T(y1-y3)= 4.9880T>T.01 SD = 0.7693T(y2-y3)= 3.6867T>T.01 SD = 0.7691回歸協(xié)方差分析結(jié)果變 異 來(lái) 源平方和自由度均方F值總 回 歸170.095725離 回 歸57.1552212.7217誤 差112.9405428.235110.3742*回歸系數(shù)間41.6685220.83437.6549*回歸截距間71.2719235.63608.2938*共同回歸系數(shù)98.8238234.2967SIG. 5%, SI

9、G. 1%（5）調(diào)整處理平均(回歸):處 理平均值調(diào)整后均值A(chǔ)1B125.222225.1130A2B124.111124.1111A3B121.166721.2759T-測(cè)驗(yàn)結(jié)果(回歸):T(y1-y2)=1.0252NO SIG.SD =0.9772T(y1-y3)=3.9255T>T.01SD =0.9775T(y2-y3)=2.9013T>T.05SD =0.9772各個(gè)處理的調(diào)整值處理 重復(fù)1 重復(fù)2 重復(fù)3 重復(fù)4 重復(fù)5 重復(fù)6 重復(fù)7 重復(fù)8 重復(fù)9 A1B1 28.403223.799021.773023.229527.738226.368523.264325.1

10、94826.2469A2B1 25.351121.246921.720925.264326.299025.825123.694826.368521.2295A3B1 21.368519.264319.929322.203522.660118.981421.264323.642722.16883、對(duì)下表數(shù)據(jù)進(jìn)行通徑分析，繪制通徑分析圖和通徑分析表，解釋說(shuō)明結(jié)果20%解答：由DPS計(jì)算可得，計(jì)算結(jié)果當(dāng)前日期 2014/7/7 11:11:09變量平均值標(biāo)準(zhǔn)差膨脹系數(shù)VIFx11.74750.5875.2352x240.169.30892.0721x30.30410.18632.7686x438.0

11、53.64513.1183x52.19750.84464.2156y8.1922.5519相關(guān)系數(shù)(右上角為顯著水平)x1x2x3x4x5yx110.02920.00010.00010.00010.0001x20.487710.01070.00260.0040.0117x30.74790.557310.00040.00250.0043x4-0.7501-0.635-0.71710.00040.0001x50.83760.61410.6369-0.712410.0001y0.80770.55170.6099-0.77390.88181方差分析表方差來(lái)源平方和df均方F值p-值回 歸102.604

12、4520.520913.59540.0001剩 余21.1317141.5094總 的123.7361196.5124相關(guān)系數(shù)R=0.910615決定系數(shù)RR=0.829220調(diào)整相關(guān)R'=0.876486變量x 回歸系數(shù) 標(biāo)準(zhǔn)系數(shù) 偏相關(guān) 標(biāo)準(zhǔn)誤 t值 p-值 b0 12.85516.79211.89270.0779b1 0.53640.12340.12941.09860.48830.6324b2 -0.0160-0.0583-0.09760.0436-0.36680.7189b3 -1.2784-0.0933-0.13452.5174-0.50790.6189b4 -0.2315-

13、0.3306-0.41270.1365-1.69520.1107b5 1.92840.63820.60110.68522.81430.0131剩余標(biāo)準(zhǔn)差sse= 1.2286Durbin-Watson d= 1.6899序號(hào)觀察值擬合值殘差標(biāo)準(zhǔn)殘差學(xué)生殘差cook距離17.678.4668-0.7968-0.6545-0.72680.0205211.7512.1965-0.4465-0.3668-0.43690.013336.858.2205-1.3705-1.1258-1.20260.03449.810.0759-0.2759-0.2266-0.3790.04358.057.38380.66

14、620.54720.60380.0132610.2510.5965-0.3465-0.2846-0.34550.009471311.71581.28421.05491.20230.07289.3410.0587-0.7187-0.5904-0.74540.05596.98.4483-1.5483-1.2718-1.69920.37781010.110.226-0.126-0.1035-0.11470.00051112.9510.82482.12521.74571.95980.1666126.45.70570.69430.57030.67220.0293137.037.0563-0.0263-0

15、.0216-0.02390146.926.8630.0570.04680.050.0001155.174.73250.43750.35930.43580.0149163.14.0103-0.9103-0.7477-1.01190.1419175.626.8816-1.2616-1.0363-1.21820.0944186.977.6945-0.7245-0.5951-0.690.0273198.46.22182.17821.78921.95820.1265207.578.0797-0.5097-0.4186-0.48670.0139作用因子直接作用通過x1通過x2通過x3通過x4通過x5x10

16、.26330.0717-0.33790.25670.5434x20.15290.1235-0.33060.20560.3651x3-0.41580.21390.12150.26890.5196x4-0.3381-0.1999-0.09290.3307-0.4668x50.64520.22180.0865-0.33490.2446剩余通徑系數(shù)=0.435118預(yù)測(cè): 預(yù)報(bào)因子：x1=1.7136，x2=40.2636，x3=0.2862，x4=38.2500，x5=2.1273置信水平：=0.05點(diǎn)Y估計(jì)：8.139 (7.5868.692)Y預(yù)測(cè)值：8.139 (5.48610.792)從通徑

17、系數(shù)分析表可以看出，x5即結(jié)果數(shù)的通徑系數(shù)最大，表明結(jié)果數(shù)是影響產(chǎn)量的主要因子，在間接效應(yīng)中，x3即主莖數(shù)通過x5即結(jié)果數(shù)的間接效應(yīng)為最大，表明主莖數(shù)是一個(gè)重要的間接效應(yīng)。通徑圖：X1X3X4YX5X24、對(duì)以下資料進(jìn)行聚類分析，劃出聚類圖，并解釋說(shuō)明分析結(jié)果20%解答：由DPS計(jì)算可得，計(jì)算結(jié)果當(dāng)前日期 2014/7/7 10:21:52數(shù)據(jù)標(biāo)準(zhǔn)化-1.6170.0674-1.02550.8122-1.463-0.7542-0.6972-0.3697-1.309-0.0401-0.20481.8506-1.1550.1441-1.31270.3354-1.001-0.07850.4791.0

18、515-0.847-1.2686-1.05960.7513-0.6931.37261.2175-0.727-0.539-1.4221-1.24430.391-0.3850.89650.95770.6098-0.231-0.5008-0.47840.4232-0.0770.32070.3080.69610.0770.60481.29960.97240.231-1.3684-0.8203-0.50350.3851.61061.3817-0.64020.5391.10381.2654-1.69880.6930.96560.3901-0.5990.847-0.9307-1.1485-0.61291.0

19、010.47430.9714-0.61191.1550.5511.1286-0.12891.3090.39750.6294-0.94331.4630.1288-0.875-2.29121.617-2.2743-1.16221.2328歐氏距離 距離矩陣(下三角) 6.39325.69422.80727.98217.50957.0868聚類結(jié)果 T I J 距離 1322.80722215.69423417.0868系統(tǒng)聚類圖中各樣本次序 1 2 3 4 劃出聚類圖5、對(duì)以下資料進(jìn)行主成分分析，并解釋說(shuō)明分析結(jié)果20%19962006年糧食總產(chǎn)量及其影響因子數(shù)據(jù)指標(biāo)X1X2X3X4X5X6X7X

20、8X9Y199659.47108.35370. 16104. 18369. 3645. 143. 2197. 2422. 51246. 30199759. 96109. 22369. 91101. 42397. 0845. 640. 4105. 822. 521271. 90199860. 03110. 14368. 5102. 15381. 2646. 241. 77105. 2222. 491319. 50199960. 78110. 96362. 13104. 89394. 9644. 545. 6108. 4422. 531399. 25200061. 62112. 05356. 68

21、103. 62416. 3643. 149. 75112. 0922. 551467. 80200162. 31112. 78358. 0499. 85431. 3142. 547. 21120. 0422. 551486. 30200263. 04113. 52345. 3607. 97445. 3542. 653. 52125. 122. 61424. 74200363. 8114. 81335. 91104. 21433. 9143. 473. 17129. 2122. 921471. 01200464. 56115. 02329. 67102. 71516. 9244. 486. 41

22、37. 2422. 941509. 50200565. 04116. 34326. 27101. 79559. 3241. 2105. 53142. 6523. 011514. 93200665. 45117. 21327. 4697. 66630. 192. 7142. 59148. 3623. 041542. 20X1：等宜耕地面積(萬(wàn)公頃)；X2：等宜耕地面積(萬(wàn)公頃)；X3：等宜耕地面積(萬(wàn)公頃) ；X4：不宜耕地面積(萬(wàn)公頃)；X5：農(nóng)業(yè)產(chǎn)值(億元) ；X6：工業(yè)產(chǎn)值比例(% )；X7：林業(yè)產(chǎn)值(億元) ；X8：化肥施用量(萬(wàn)噸)；X9：農(nóng)田水利化水平(萬(wàn)公頃)解答：（1）由DPS計(jì)

23、算可得，計(jì)算結(jié)果當(dāng)前日期 2014-7-11 10:01:43一般線性回歸分析：變量平均值標(biāo)準(zhǔn)差膨脹系數(shù)VIFx11834.25577.6476801566.6511x257.171718.121942705.3369x3103.366732.670762623.6486x4320.8408102.426414095.8084x585.870838.339217.7447x6414.6683152.32651826.5917x736.77516.617470.3765x860.762536.77191011.6773x9110.949238.46684431.9536x1020.80426.5

24、552387553.4421y1304.4525422.1246（2）相關(guān)系數(shù)如下表：相關(guān)系數(shù)(右上角為顯著水平)x1x2x3x4x5x6x7x8x9x10yx110.00010.00010.00010.01050.00030.01220.080.00010.00010.0001x20.994110.00010.00010.0130.00010.02270.03860.00010.00010.0001x30.99680.999510.00010.0120.00010.01980.04720.00010.00010.0001x40.98560.96170.969310.00990.00330.0

25、0540.20820.00080.00010.0001x50.70480.68990.69560.708710.04030.10930.17520.03690.010.0148x60.85980.90450.89350.77130.597410.32050.00020.00010.00020.0001x70.69470.64780.6590.74560.48590.313810.68190.14050.01430.0389x80.52440.60130.58180.39150.4190.873-0.13210.0020.06620.0233x90.91060.94950.94010.82940

26、.60550.98110.45170.795410.00010.0001x100.99960.99640.99840.98070.70760.87190.68340.54610.920710.0001y0.97430.99050.98780.92790.68090.92550.60060.64590.96810.97831（3）方差分析表方差分析表方差來(lái)源平方和df均方F值p-值回 歸19600201019600231800.0138剩 余61.6358161.6358總 的196008111178189得出相關(guān)系數(shù)R=0.999984；決定系數(shù)RR=0.999969；調(diào)整相關(guān)R'=0

27、.999828變量x回歸系數(shù)標(biāo)準(zhǔn)系數(shù)偏相關(guān)標(biāo)準(zhǔn)誤t值p-值b007.850800.9999b16.04968.27850.8553.66881.64890.2409b211.92790.51210.404226.9930.44190.7018b332.29832.49980.87218.1311.78130.2168b4-8.3659-2.0299-0.95022.7438-3.0490.0928b51.66550.15130.9880.26016.40360.0235b60.56080.20240.64510.66410.84430.4874b7-2.9951-0.1179-0.92881.

28、195-2.5060.1291b8-3.139-0.2734-0.83762.0475-1.5330.265b9-2.8742-0.2619-0.57434.0967-0.7020.5556b10-523.175-8.1244-0.9188224.8-2.3270.1454特征向量(轉(zhuǎn)置)x1x2x3x4x5x6x7x8x9x10z10.35050.35340.3530.33770.26310.32530.22330.22470.33830.3518z2-0.1001-0.0248-0.044-0.212-0.0870.3218-0.6110.63860.2087-0.081z3-0.0825

29、-0.1106-0.101-0.0410.9508-0.095-0.1330.0577-0.17-0.078z4-0.2204-0.0807-0.129-0.4660.06260.11850.70150.30660.2721-0.181z50.1119-0.1144-0.0820.2614-0.123-0.1030.24120.5948-0.6670.1295z6-0.0838-0.2071-0.2050.20940.01220.84450.0746-0.26-0.237-0.148z7-0.117-0.4703-0.3290.608-0.011-0.1970.03940.11570.4821

30、-0.037z8-0.1863-0.19350.75190.197-0.006-0.0240.03520.0688-0.043-0.562z9-0.310.7352-0.290.3112-0.004-0.0580.02220.0683-0.023-0.416z100.8048-0.0261-0.201-0.0660.0032-0.0330.00190.02070.0551-0.55自變量主成分得分NoZ(i,1)Z(i,2)Z(i,3)Z(i,4)yN(1)-8.83510.47010.1250.09190N(2)0.3634-0.98340.3566-0.261246.3N(3)0.4883

31、-0.94110.2186-0.191271.9N(4)0.4765-0.97580.244-0.1661319.5N(5)0.5587-0.79610.3036-0.1471399.3N(6)0.6462-0.59650.2535-0.1151467.8N(7)0.725-0.54020.1091-0.1131486.3N(8)0.1926-0.1465-2.194-0.1091424.7N(9)1.0109-0.04090.19750.2911471N(10)1.3410.38560.08240.58571509.5N(11)1.56340.96010.05810.68561514.9N(

32、12)1.46933.20470.2455-0.5541542.2主成分回歸分析分析結(jié)果：方差分析表方差來(lái)源平方和df均方F值p-值回 歸19273104481828102.920.0001剩 余32770.7674681.5總 的196008111178189得出相關(guān)系數(shù)R=0.991605；決定系數(shù)RR=0.983281；調(diào)整相關(guān)R'=0.986776變量z回歸系數(shù)標(biāo)準(zhǔn)系數(shù)偏相關(guān)標(biāo)準(zhǔn)誤t值p-值b01304.45319.75266.0430.0001b1147.99120.98810.99157.319920.2180.0001b213.23190.03740.27817.2840

33、.76560.4659b3-45.0623-0.0744-0.49929.606-1.5220.1665b49.81770.00830.064157.7490.170.8692剩余標(biāo)準(zhǔn)差sse=68.4218Durbin-Watson d=0.8721標(biāo)準(zhǔn)化回歸方程：標(biāo)準(zhǔn)化變量系數(shù)std(xi)的表達(dá)式:52.104505std(x1)std(x1)=(x1-1834.2500)/577.647656.155589std(x2)std(x2)=(x2-57.1717)/18.121954.924213std(x3)std(x3)=(x3-103.3667)/32.670744.460669std(x4)std(x4)=(x4-320.8408)/102.4264-4.442973std(x5)std(x5)=(x5-85.8708)/38.339257.862062st