1、部分习题部分习题P47/1(1)总体是指所研究的总体是指所研究的金针虫金针虫总体；总体；(2)样本是指从金针虫总体中随机抽取的样本是指从金针虫总体中随机抽取的6个个体个个体组成组成的样本；的样本；(3)变数是指金针虫的变数是指金针虫的头数头数；(4)观察值是指变数的观察值是指变数的6个取值个取值为为6个观察值。个观察值。组组 限限组中值（组中值（y）划线计数划线计数 次数（次数（）24.5 27.526227.5 30.529 730.5 33.532 2433.5 36.535 4136.5 39.538 2139.5 42.541442.5 45.54445.5 48.5471P47/2
2、极差=46-26=20；组数=7；组距=20/7=2.85713 100个小区水稻产量资料的次数分布表个小区水稻产量资料的次数分布表05101520253035404512345678 100个小区水稻产量资料的方柱形图P47/305101520253035404512345678P47/4222222/(374634)/1003485/10034.85()/374634)3485/1003.221100 1yy nyynSn222/(2 267 291 47)/1003467/10034.67()/1212973467/1003.331100 1yfyffyfyfSf P47/5等级差法:假
3、定y0=35，02222(3)7(2)1 435334.67100()/123(11)/10033.331100 1fdyyinfdfdnSin P47/6BS24：金皇后：金皇后：11112221111111122 184/(192119)/1020()/4014200/101.247110 1100%1.247/20 100%6.24%RyynyynSnSCVy22222222222222226 15 11/(16 2119)/1020()/4104 200/103.399110 1100%3.399/20 100%16.99%RyynyynSnSCVyP47/710株小麦的分蘖数为：3，
4、6，2，5，3，3，4，3，4，3。n=10，y3=2，y7=4，y2-1=y1=3，y21=61=5P47/802222(363)/1036/103.6()(33.6)(63.6)(33.6)033624()/14236/101.381.17110 1dyyyMMRyynSSnP72/2(28)0.7(19)0.9(24)68(24)(68)0.30.30.682(24)37 0.210852()(3)0.2105pypypyypypypyypp或()与()奇数被 整除P72/3 在回交后代在回交后代200株中，杂株中，杂合体非糯稻与纯合体糯稻出合体非糯稻与纯合体糯稻出现的概率各为现的概率各
5、为1/2，即杂合体，即杂合体非糯稻与纯合体糯稻各有非糯稻与纯合体糯稻各有100株。株。F1自交得自交得F2代的分离作代的分离作3:1遗传比率，即非糯稻为遗传比率，即非糯稻为0.75，糯稻为，糯稻为0.25，这一分布属离散型随机变数的概，这一分布属离散型随机变数的概率分布率分布二项式分布二项式分布。WxWxwxwxWxwxwxwxWxwxwxwx121220.750.75 0.250.1875ppq P72/4非糯稻：非糯稻：Np=20000.75=1500；糯稻：；糯稻：Nq=20000.25=500受害株数概率函数P(y)P(0)0.00100.00100.40P(1)0.01460.015
6、65.84P(2)0.08790.103535.16P(3)0.26370.3672105.48P(4)0.39550.7627158.20P(5)0.23731.000094.92调查单位为调查单位为5株的概率分布表株的概率分布表(p=0.75，q=0.25，n=400)400.00()()()yyn ynC p qp yF ynp y0055114522353325441555050.750.250.750.250.750.250.750.250.750.250.750.25CCCCCC样本平均数(成数)的抽样分布:样本总和数(次数)的抽样分布:20.75/0.75 0.25/50.037
7、5ppppq n25 0.753.755 0.75 0.250.9375npnpnpnpq P73/6(1.17)1(1.17)1 0.87900.1210(1.17)0.8790(1.17)0.1210(0.421.61)(1.61)(0.42)0.94630.66280.2835(1.610.42)(0.42)(1.61)0.33720.05370.2835p up up up upup up upup up u 11(1.610.42)(0.42)(1.61)0.66280.05370.6091(1.05)1 (1.05)(1.05)1(0.8531 0.1469)0.2938(1.05
8、)2(1.05)2 0.14690.2938(1.05)0.8531 0.14690.7062()0.051pup up up up up up up up up uuu 11.9599641.96()0.0251.9599641.96p uuuP73/7 N(16，4)112112(1020)(32)0.97730.00140.9759(12)(2)0.0228(20)1(2)10.97720.0228()0.500.6745160.674514.6517.352()0.951.96161.9612.0819.922pypup yp up yp up uuuyyyp uuuyyy=-=-=-
9、=-=-=-=-=P73/8 N=5，n=2222222525(12345)/53()/5515/52.052.01.414nNyyNNmsss=+=-=邋次数（）1.011.522.032.543.053.544.034.525.0152个样本平均数分布的次数分布表个样本平均数分布的次数分布表y1234543210123456123456789 52个样本平均数分布的次数分布图个样本平均数分布的次数分布图 平均数分布的方柱形图作正态分布。由由25个平均数构成的新总体平均数与方差个平均数构成的新总体平均数与方差:222222/75/253()/25075/251.0253/2/21.0yyyy
10、f yff yf yffnmsmmss=-=邋邋P73/9 22222/ppn pn pppqpnpq nnnpnnpqP73/10 结果为：0，1，0，0，1，1，0，1，1，02222/(010)/100.5()(00.5)(10.5)(00.5)0.5100.5/0.50.5/40.2540.52.040.50.51.0ppnpnpy nyNpq nnnpqmmsmmsmms=+=-+-+-=创=P97/40.01120.0512153.752.58161402.58130.325149.6753.75130.325149.675151.501.961001001.9697.06102.
11、941.5097.06102.94yyunyyyyyunyyyyy 或或P97/5否定无效假设，接受备择假设。否定无效假设，接受备择假设。02222220.01,9:2.50:2.50(2.38 2.382.41)/1023.90/102.39()/2.382.382.4123.9/100.068110 10.0680.02102.39 2.505.513.2500.02AyHHyyynSnSSnttP97/6 否定否定H0接受接受H01201212121212212120.05,(5)0.05,(5):5437.605.276.504.596.504.592.218(4 1)(3 1)2.2
12、182.2187.605.271.142.04431.142.015()2.571()AeyyHHnnyySSSSSSSSSSttt 一尾概率二尾概率P97/7 接受接受H01222112212012120.052461580813:0:01.9624803.746815 130.5343.74AyynynyHHuu P97/8 接受接受H0121222111222012120.05(15)222112212111263040112245:4:42.1315 40 10 4543.335 1043.3343.333.34611()()(3022)41.203.34AeyyyynySnySHHt
13、SSSSyytS P97/9 0.050.05212(29.8,2.25)101.961.64()2.250.47431029.81.9628.8730.730.474328.8730.7329.81.6430.5830.580.4743yNnuunyyyyyyyy 一尾或0.050.05212(29.8,2.25)1001.961.64()2.250.1510029.81.9629.5130.090.1529.5130.0929.81.6430.0530.050.15yNnuunyyyyyyyy 一尾或00.052:29.8:29.81.64()2.252030.10.33542030.1
14、29.80.890.335430.1 29.81.962.25/96AyyHHunyuyyunnn 一尾接受接受H0P97/10 00.05(9)2220:0:02.262(325)/1031/103.1()/16931/100.90(1)10(10 1)3.13.4440.90dAddHHtdddnSn ntH 否定去 雄28303135303430283432未去雄25282929312528273227d3226-192125否定否定H010.0520.053.1 2.262 0.901.13.12.262 0.905.1ddLdtSLdtS12012120.05(18)22112222
15、2112212:0:02.10131.26.1828.15.219 6.189 5.215.695991131.228.15.695()1.0672.90510101.067AeyyHHtySySSSSSt 去 雄28303135303430283432未去雄25282929312528273227 成组数据成组数据(t=2.905)成对数据成对数据(t=3.444)，即成组数据容易犯第二类错误第二类错误。121210.051220.0512()(31.228.1)2.101 1.0670.9()(31.228.1)2.101 1.0675.3yyyyLyytSLyytS10.0520.053
16、.1 2.262 0.901.13.12.262 0.905.1ddLdtSLdtSP97/11 12012120.0512:0:01.9642/2000.2127/1500.1842270.19711 0.19710.8029200 150110.1971 0.80290.0432001500.21 0.180.6980.043AppHppHppupppqSu 接受接受H0令令属真实差异属真实差异12nnn0.21 0.180.031212120.21 0.181.961111()0.1971 0.8029ppppppuSp qnnnn121350nnnP127/5 4组数据编 号Ti ni
17、 1 2 3 4 5 6 7 8 组1 8 10 1 6 4 7 8 2 46 5.75 8 组2 9 2 11 5.50 2 组3 6 5 0 7 3 7 28 4.67 6 组4 16 8 6 11 41 10.25 4iy1266.320iTyn组1组2组3组42222222122222111222222222232222233324222222444126793.82081011793.8270.20810246/869.59211/224.565728/637.3316861141/4iTeeeeTCnSSyCySSynySSynySSynySSsyn56.7569.5024.503
18、7.33 56.75188.08eSS两种计算方法结果完全相同。与总变异平方和完全相同。2222222222()8(5.756.3)2(5.56.3)6(4.676.3)4(10.256.3)82.1246112841793.882.128264tiiitiSSn yyTSSCn 82.12 188.08270.20teTSSSSSS种植密度(株、667)千 粒 重 123420002472582562511012253400023824424623696424160002142272212188802208000210204200210824206测定4种密度下金皇后玉米的千粒重结果P128
19、/6 iyiT3680230Ty2222222222214 4 11514 13(1)4(4 1)12368084640016247258210560810129648808245304456085304304TteTiteTtDFnkDFkDFk nTCnkSSyCCTSSCCnSSSSSS 方 差 分 析 表25.332.524eMSSEn变异来源DF SS MS F F0.05 F0.01 处 理 间35304176869.79*3.495.95误 差1230425.33 总 变 异155608 多重比较时的LSRa值计算 种植密度的差异显著性(SSR测验)结论结论：金皇后玉米的千粒重在
20、不同的密度下有极显著的差异，种植密度愈高千粒重愈低。p SSR0.05SSR0.01LSR0.05LSR0.0123.084.327.7610.8933.234.558.1411.4743.334.688.3911.79 处 理 平均千粒重 差异显著性 5%1%2000 253 a A 4000 241 b B 6000 220 c C 8000 206 d D P128/7 3个稻田的农药残留量iyT=27.01213 3 2 11713 12(1)3(3 1)6(1)3 3(2 1)9TteeDFlmnDFlDFl mDFlm n 稻 田123水 样123123123残留量1.11.31.
21、21.31.31.41.82.12.21.21.11.01.41.51.22.02.01.9水样Tij2.32.42.22.72.82.63.84.14.1稻田Ti6.98.112.0稻田平均1.151.352.00222222222222222122227.040.5181.11.31.940.543.0840.52.586.98.112.040.5642.8740.52.372.32.44.142.87242.9242.870.0543.0842TitijieijeTClmnSSyCTSSCmnTTSSnmnTSSyn.920.16方差分析表变异来源DFSSMSFF0.05F0.01稻 田
22、 间22.371.19148.7*5.1410.92水 样 间60.050.0081水 样 内90.160.018总 变 异172.5810.0080.03656eMSSEmn多重比较时的LSRa值计算 种植密度的差异显著性(SSR测验)结论结论：水样间无显著差异；稻田间有极显著的差异，稻田3农药污染最重，稻田2次之，稻田1最轻。p SSR0.05SSR0.01LSR0.05LSR0.0123.465.240.12630.191333.585.510.13070.2011处 理 平均残留量 差异显著性 5%1%稻 田 3 2.00 a A 稻 田 2 1.35 b B 稻 田 1 1.15 c
23、 C P128/8 5个水稻品种干物质的干物质积累量525517.4lmnT品种样点干物质重量TijTi甲17.88.99.211.410.547.899.29.92212.110.68.79.910.151.4乙37.48.88.97.89.842.776.47.6446.26.65.37.58.133.7丙512.610.211.411.812.158.1126.112.61615.215.112.312.512.968.0丁75.84.76.67.47.932.468.86.8886.46.88.17.27.936.4戊913.815.113.412.616.671.5146.914.6
24、91011.717.215.615.115.871.4iy122222222222215 2 5 14915 14(1)5(2 1)5(1)5 2(5 1)40517.45354.0552507.88.915.85880.62 5354.0552526.564899.276.4126.168.81TteeTitDFlmnDFlDFl mDFlm nTClmnSSyCCTSSCmn 222222122246.9105789.1860 5354.0552435.130847.851.475.45789.186055811.5040 5789.186022.31805880.62 5811.5046
25、9.1160ijieijeCTTSSnmnTSSyn方差分析表14.46360.668110eMSSEmn变异来源DFSSMSFF0.05F0.01品 种 间4435.1308108.782724.37*5.1911.39样 点 间522.31804.46362.58*2.453.51样 点 内4069.11601.7279总 变 异49526.5648多重比较时的LSRa值计算 5个水稻品种干物质的差异显著性(SSR测验)结论：结论：5个水稻品种间有极显著的差异。其中，戊与丙、甲与乙、乙与丁间无显著差异；戊与甲、乙、丁间达极显著水平。p SSR0.05SSR0.01LSR0.05LSR0.0
26、123453.643.743.793.835.705.966.116.182.432.502.532.563.813.984.084.13处 理 平均干物质量差异显著性 5%1%戊丙甲乙丁14.6912.619.927.646.88a a b bc c A AB BC C CP128/9 5个小麦品种的黑穗病率（%）反正弦转换2214 5 11914 13357.3(1)4(5 1)166383.1620TteDFnkDFkTDFk nCnk ABCDABCD0.84.09.86.05.1311.5418.2414.183.81.956.279.811.247.9248.5663.290.00
27、.766.07.00.004.8054.3315.346.03.510.384.614.1810.7818.7266.891.73.29.22.87.4910.3017.669.63Ti12.313.3151.5180.238.0445.34157.51169.33T=357.3T=410.22方差分析表方差分析表结论结论：品种间差异不显著。2222222220.84.02.86383.16 15132.65/(12.313.3151.5180.2)/5 6383.164767.3315132.65 4767.33 10365.32TtieTtSSyCSSTn CSSSSSS变异来源DFSSM
28、SFF0.05品 种 间34767.331589.112.45 3.24误 差1610365.32647.83总 变 异1915132.65方差分析表方差分析表结论结论：数据转换后,品种间差异显著。说明转换后各品种的均方得到改进，从而提高了测验的灵敏度。22222222222/410.22/208414.025.1311.549.638414.027750.90/(38.0445.34157.51169.33)/5 8414.022982.947750.90 2982.944767.96TtieTtCTnkSSyCSSTn CSSSSSS变异来源DFSSMSFF0.05品 种 间32982.9
29、4994.313.34*3.24误 差164767.96298.00总 变 异197750.09P143/1接受接受H0：差异不显著：差异不显著0220.975(9)0.025(9)22:3.6:3.60.052.7019.02(10 1)4.511.253.60.05AHHxxsxpP143/26个方差同质性测验的计算 133.644134.563.515714.0628214.27457.082.658210.6328316.94467.762.829711.318841.2845.120.24690.987652.56410.240.94003.760062.0448.160.71292
30、.8516 24282.9210.903443.61362222lnlniiiiiiiiSSSS2222220126126220.975(5)0.025(5)2222:,0.8312.83282.9211.788324ln24 ln11.788359.21061111111.09723(6 1)444241(59.210643.6136)14.21521.0972AiipiipcHHxxSSSCxp 不全等0.05否定否定H0：差异显著：差异显著P143/3测验下表各样本观察次数是否适合各相应的理论比率222222*22222232/3134 3 362/(3 170)1.129432/324
31、0 3 1202/(3 360)12.89261/76 561/1322.7348158/15240 15 138/(15 253)0.3607ccccxAanxAanxA anxAan 样本号理论比率观察次数A an3:13:11:115:113424076240 36 120 56 13170360132253P144/4接受接受H0：差异不显著：差异不显著02220.05(2)22222:9:3:4:9:3:4348 115 1576205.993481151576200.04089/16 6203/16 6204/16 6200.05AiiHFHFnxaxnmnp分离符合的比率分离不符
32、合的比率P144/5200个稻穗粒数分布与正态分布的适合性测验个稻穗粒数分布与正态分布的适合性测验220.05(9)20054.8510.081.954716.92nySxx每每 穗穗 粒粒 数数次数次数(O)理论次数理论次数(E)组限组限(y)组中点组中点25.530.5281-24.35-2.420.00781.560.201030.535.5333-19.35-1.920.01963.920.215935.540.53810-15.35-1.420.050410.080.000640.545.54321-9.35-0.930.098419.680.087245.550.54832-4.3
33、5-0.430.157431.480.008650.555.553410.650.060.190338.060.227155.560.558385.650.560.188437.680.002760.565.5632510.651.060.143128.620.457965.570.5681615.651.550.084016.800.038170.575.573820.652.050.04048.080.000875.580.578325.652.540.01472.940.001280.585.583230.653.040.00551.110.7136yyyySp2xP144/6接受接受H
34、0：差异不显著：差异不显著02220.05(3)2222212342222:9:3:3:1:9:3:3:11324238 142267.8116(339)916(1323 423 389 14)2260.64309 2260.05AHFHFnxaaaaxnnp 分离符合的比率分离不符合的比率P144/7杂交F3代在室内与田间对某种病害反应的相关研究H0:两个变数相互独立；HA:两个变数彼此相关222220.01(4)(142 37.99)(51 114.21)(17643.57)1127.9537.99114.2143.5713.280.05xxp否定否定H0：差异极显著：差异极显著田 间 反
35、 应温 室 幼 苗 反 应Ri抗 病分 离感 病抗 病142(37.99)51(114.21)3(43.80)R1=196分 离13(81.21)404(244.16)2(93.63)R2=419感 染2(37.80)17(113.63)176(43.57)R3=195CiC1=157C2=472C3=181n=810P144/8测验以下4个样本的分离是否一致符合3：1的分离比率222221.3255 13.333321.373753.229289.26176903 2250.08203 91598.26170.082089.1797iTiTxxxx 20.05(1)20.05(2)20.05
36、(3)3.845.997.81xxx样本号理论比率观 察 次 数Aan3:1134361701.32550.788228.383:124012036013.33330.666780.001:1765613221.37370.333332.2415:12401325353.22920.948612.34合合 计计6902259152x p npq6个方差同质性测验的计算否定否定H0：极显著：极显著22240847.0383/91144.8376ln911 ln44.83763464.575911111111.00213(4 1)1693591312529111(3464.57593226.697
37、8)237.37961.0021pipSsCx 20.05(3)7.81x 128.37991694796.20313.3457565.4201279.996035928718.56404.38201573.1296332.24161314223.64963.4733454.9967412.33582523108.62162.5125633.1514 91140847.038313.71353226.69782222lnlniiiiiiiiSSSSP246/12.6（一）（一）1.F测验测验 表表 1 1 方差分析表方差分析表变异来变异来源源平方和平方和自由度自由度均方均方F F值值0.050
38、.050.010.01区组间区组间0.27120.27123 30.09040.09041.0631.0633.293.295.425.42处理间处理间8.97218.97215 51.79441.794421.0921.092.902.904.564.56误差误差1.27621.276215150.08510.0851总变异总变异10.519610.519623232.多重比较多重比较处理处理均值均值5%5%显著显著水平水平1%1%极显著水平极显著水平处理处理6 67.5500007.550000 a aA A处理处理5 57.1257.125 ababABAB处理处理3 36.900000
39、6.900000 b b BCBC处理处理1 16.456.45 c c CDCD处理处理2 26.26.2 c c DEDE处理处理4 45.75.7 d d E E（二）（二）1.F测验测验方差分析表方差分析表变异来源变异来源 平方和平方和自由度自由度均方均方F F值值0.050.050.010.01处理间处理间8.97218.97215 51.79441.794420.87220.8722.77 4.252.77 4.25处理内处理内1.54751.547518180.0860.086总变异总变异10.519610.519623232.多重比较多重比较处理处理均值均值5%5%显著水显著水
40、平平1%1%极显著水平极显著水平F F7.55000017.5500001 a aA AE E7.1257.125 ababABABC C6.90000016.9000001 b b BCBCA A6.44999986.4499998 c c CDCDB B6.19999986.1999998 c c DEDED D5.69999985.6999998 d d E EP246/12.71.F测验测验拉丁方试验方差分析表拉丁方试验方差分析表变异来变异来源源平方和平方和自由度自由度均方均方F F值值F F0.05 0.05 F F0.010.01纵列纵列44.5644.564 411.1411.1
41、43.87703.87703.26 5.413.26 5.41横行横行8.568.564 42.142.140.744780.744783.26 5.413.26 5.41处理处理202.16202.164 450.5450.5417.58917.5893.26 5.413.26 5.41误差误差34.4834.4812122.87332.8733总和总和289.76289.7624242.多重比较多重比较 字母标记表示结果字母标记表示结果处理处理均值均值5%5%显著水显著水平平1%1%极显著水平极显著水平处理处理A A27.827.8a aA A处理处理C C26.226.2a aA A处理
42、处理B B25.625.6a aA A处理处理D D22.222.2 b b B B处理处理E E2020 b b B BP297/13.31.F测验测验方差分析表方差分析表(固定模型固定模型)变异来变异来源源平方和平方和自由度自由度均方均方F F值值0.010.01区组间区组间1.166671.166672 20.583330.583331.87811.87813.443.445.725.72A A因素间因素间57.333357.33333 319.111119.111161.52961.5293.053.054.824.82B B因素间因素间8.6666678.6666672 24.333
43、334.3333313.95113.9513.443.445.725.72AxBAxB2 26 60.333330.333331.07321.07322.552.553.763.76误差误差6.833336.8333322220.3106060.310606总变异总变异767635352.多重比较多重比较因素间字母标记表示结果因素间字母标记表示结果处理处理均值均值5%5%显著水显著水平平1%1%极显著水平极显著水平A4A415.88888915.888889a aA AA3A314.33333314.333333 b b B BA2A213.22222213.222222 c c C CA1A
44、112.55555512.555555 d d C C因素字母标记表示结果因素字母标记表示结果处理处理均值均值5%5%显著显著水平水平1%1%极显著水平极显著水平B3B314.514.5a aA AB1B114.1666714.16667a aA AB2B213.3333313.33333 b b B B2.多重比较多重比较组合字母标记表示结果组合字母标记表示结果处理处理均值均值5%5%显著水平显著水平1%1%极显著水平极显著水平121216.66666716.666667 a aA A101015.66666715.666667 b bABAB111115.33333315.333333 b
45、 bABAB7 714.66666714.666667 bcbc BCBC9 914.66666714.666667 bcbc BCBC8 813.66666713.666667 cdcd CDCD4 413.66666713.666667 cdcd CDCD6 613.33333313.333333 d d CDCD3 313.33333313.333333 d d CDCD1 112.66666712.666667 d d DEDE5 512.66666712.666667 d d DEDE2 211.66666711.666667 e e E EP297/13.41.F测验测验 方差分析
46、表方差分析表变异来源变异来源 平方和平方和自由度自由度均方均方F F值值F F0.05 0.05 F F0.010.01区组区组0.16670.16672 20.08330.0833因素因素A A40.333340.33331 140.333340.333369.14369.14318.5 98.518.5 98.5误差误差1.16671.16672 20.58330.5833因素因素B B75751 1757530306.39 15.986.39 15.98AxBAxB3 31 13 31.21.26.39 15.986.39 15.98误差误差10104 42.52.5总和总和129.66
47、7129.66711112.多重比较多重比较主处理字母标记表示结果主处理字母标记表示结果处理处理均值均值5%5%显著水平显著水平1%1%极显著水平极显著水平主处理主处理1 17.66666657.6666665 a aA A主处理主处理2 24 4 b bA A2.多重比较多重比较副处理字母标记表示结果副处理字母标记表示结果处理处理均值均值5%5%显著水平显著水平1%1%极显著水平极显著水平副处理副处理1 18.3333338.333333 a aA A副处理副处理2 23.33333333.3333333 b b B BP190/9.5回归方程回归方程y=-0.00571+0.02343xy=-0.00571+0.02343x相关系数相关系数R=0.999554R=0.999554决定系数决定系数R R2 2=0.999108=0.999108t=74.85 t0.05=2.571Sy/x=0.00828078671210825P190/9.5ny=33.29539+0.7456xy=33.29539+0.7456xn相关系数相关系数R=0.842384R=0.842384n决定系数决定系数R2=0.709610nt=3.51nSy/x=4.96
