高級生物統(tǒng)計

1、高級生物統(tǒng)計試題1、論述試驗數(shù)據(jù)為什么要進行統(tǒng)計分析？（結合實際例子）20%答：（1）在試驗研究中，通過觀察、測量和記載，可獲得大量的數(shù)據(jù)資料。但這些資料往往是零亂的、無規(guī)律可循，只有通過對試驗數(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）試驗普遍存在試驗誤差，用生物統(tǒng)計方法來分析試驗資料，降低試驗誤差，提高試驗的精確性，以正確估計誤差，得到可靠的試驗結論。（3）統(tǒng)計分析 解決“試驗結果怎么看”的問題。能夠?qū)υ囼灁?shù)據(jù)用統(tǒng)計分析方法正確地估計出試驗誤差和處理效應，達到試驗的預期目的。 例如，達爾文應用統(tǒng)計學方法研究了生物的連續(xù)變異現(xiàn)象；孟德爾應用分組統(tǒng)計方法發(fā)現(xiàn)了遺傳學中的分離定律和獨立分配定律

2、；Karl Pearson用統(tǒng)計方法研究進化問題；Galton用回歸分析方法研究了親子身高的遺傳規(guī)律。 到了20世紀初，R. A. Fisher提出了方差分析方法，建立了試驗設計三大原理，并提出了隨機區(qū)組和拉丁方等試驗設計方案，出版了經(jīng)典的“Statistical Methods for Research Workers”一書，奠定了生物統(tǒng)計學的基礎。 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)計推斷理論的建立上做出了重要貢獻，推動了數(shù)理統(tǒng)計學的發(fā)展，同時也推動

3、了生物統(tǒng)計學的發(fā)展。 2、試驗有兩種不同的飼料添加劑和對照三處理，重復9次，有27頭豬參與試驗，兩個月增重資料如下。各個處理供試豬初始體重見表，試對資料進行分析。解釋說明結果。20%飼料添加劑對豬增重試驗結果表 (單位：kg)處 理2號添加劑1號添加劑對照觀測指標初重x增重y初重x增重y初重x增重y觀測值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）試驗資料的數(shù)學模型eij+be+ti+my(xij-mx)=yij觀測值不僅具有飼料效應和隨機誤差，而且還受到初重的影響。故單因素完全隨機設計試驗資料觀測值的數(shù)據(jù)結構式為:(i=1,2,L,k;j=1,2,L,n)（2）計算回歸系數(shù)并進行顯著性檢驗 be=SPSS=0.9832回歸系數(shù)由誤差項的統(tǒng)計數(shù)計算：由DPS軟件計算回歸方程系數(shù)B結果如下： 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、對矯正每只豬增重進行方差分析 （1）矯正每只豬增重的方差分析表變異來源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的各項自由度、平方和與乘積和因子間協(xié)方差分析結果方 差 來 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）回歸誤差項方差分析方差來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平方和及自由度調(diào)整各個處理平均(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-測驗 T-測驗結果(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)方差分析結果變 異 來 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A1B125.222225.1130A2B124.111124.1111A3B121.166721.2759T-測驗結果(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各個處理的調(diào)整值處理 重復1 重復2 重復3 重復4 重復5 重復6 重復7 重復8 重復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、對下表數(shù)據(jù)進行通徑分析，繪制通徑分析圖和通徑分析表，解釋說明結果20%解答：由DPS計算可得，計算結果當前日期 2014/7/7 11:11:09變量平均值標準差膨脹系數(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相關系數(shù)R=0.910615決定系數(shù)RR=0.829220調(diào)整相關R'=0.876486變量x 回歸系數(shù) 標準系數(shù) 偏相關 標準誤 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剩余標準差sse= 1.2286Durbin-Watson d= 1.6899序號觀察值擬合值殘差標準殘差學生殘差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預測: 預報因子：x1=1.7136，x2=40.2636，x3=0.2862，x4=38.2500，x5=2.1273置信水平：=0.05點Y估計：8.139 (7.5868.692)Y預測值：8.139 (5.48610.792)從通徑

17、系數(shù)分析表可以看出，x5即結果數(shù)的通徑系數(shù)最大，表明結果數(shù)是影響產(chǎn)量的主要因子，在間接效應中，x3即主莖數(shù)通過x5即結果數(shù)的間接效應為最大，表明主莖數(shù)是一個重要的間接效應。通徑圖：X1X3X4YX5X24、對以下資料進行聚類分析，劃出聚類圖，并解釋說明分析結果20%解答：由DPS計算可得，計算結果當前日期 2014/7/7 10:21:52數(shù)據(jù)標準化-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、對以下資料進行主成分分析，并解釋說明分析結果20%19962006年糧食總產(chǎn)量及其影響因子數(shù)據(jù)指標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(萬公頃)；X2：等宜耕地面積(萬公頃)；X3：等宜耕地面積(萬公頃) ；X4：不宜耕地面積(萬公頃)；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(萬噸)；X9：農(nóng)田水利化水平(萬公頃)解答：（1）由DPS計

23、算可得，計算結果當前日期 2014-7-11 10:01:43一般線性回歸分析：變量平均值標準差膨脹系數(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）相關系數(shù)如下表：相關系數(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得出相關系數(shù)R=0.999984；決定系數(shù)RR=0.999969；調(diào)整相關R'=0

27、.999828變量x回歸系數(shù)標準系數(shù)偏相關標準誤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果：方差分析表方差來源平方和df均方F值p-值回 歸19273104481828102.920.0001剩 余32770.7674681.5總 的196008111178189得出相關系數(shù)R=0.991605；決定系數(shù)RR=0.983281；調(diào)整相關R'=0.986776變量z回歸系數(shù)標準系數(shù)偏相關標準誤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剩余標準差sse=68.4218Durbin-Watson d=0.8721標準化回歸方程：標準化變量系數(shù)std(xi)的表達式: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