ANOVA分析例题

1、Single（ 7）单因素单向分组方差分析例1、北京农业大学从南斯拉夫引进15个T型恢复材料，为了研究其应用价值，以农大139为对照，进行了个农艺性状表现的观察。其中6个恢复材料和农大139各5个单株抽穗期观察结果如表1 :引进恢复系抽穗期观察资料恢复系-单株抽穗期12345PI2770161111101211Lot-11313121414Texas1212131212zgR2806-781312121313zgR2268-781819181819vk-64-281918201919农大1391011101110例2、5个玉米品种的盆栽试验，调查了穗长（ cm）性状，得资2，试检验品种穗长间有

2、无差异。（各处理的重复数不等）表25个玉米品种的穗长B121.519.5202218206B21618.51715.520166B31917.520181752118.519204B515.51817164品种穗长（cm）重复数例3、表3为同一公猪配种的3头母猪所产的各头仔猪的断奶时（每组样本容体重（斤），试分析母猪对仔猪体重效应的差异显著性。量不等）表3二头母猪的仔猪断奶时体重母猪别ni观察值No.182422.5242022232222.5No.271919.52023.5192116.5No.39161615.520.51417.514.515.519单因素双向分组方差分析小区内没有重复

3、观察值例4、5个水稻品种的产量比较试验，随机区组设计，4次重复，获得每个小区产量（Kg）资料如表4所示：试分析这 5个水稻品种间产量水平有无显著差异。表4水稻5个品种的每区产量（Kg）例5、将一种生长激素配成 M1、M2、M 3、IVI4、M4、M5五种浓度，并用Hl、H2、H3、种时间浸渍某大豆品种的种子，45天后得各处理每口础区组（重复）InrnIV农海6753525051十石52585557农林8758565353农林1853515455植株的平均干物重（g）于下表5,试作方差分析。表5生长激素对大豆干重的影响M（生长激素）H （时间）HHbM1131414M2

4、121213M3333M410910M5254小区内有重复观察值例6、北京农业大学以4X 5的两个亲本杂交设计研究亲本配合力，随机区组设计 3次重复，从样段内随机抽取 10株进行考种，其5个组合和对照农大 139的结实小穗数部分资料如下表6:（部分是指其中5个组合+CK 3次重复，每小区5株的考种数据。）表6两组亲本杂交结实小穗数部分资料重复&合In123451234512345115161715161515151615151415161621515161515151514151615141516163141415131416161416151614151516415161615161

5、51615161515171714155161717171716171817171819171718农大139141413121213131212121212141313例7、对A、B、C、D、E 5个杂优水稻品种的干物质积累过程进行了系统的测定，随机区组设计，2次重复，每小区5株观察数据。试作方差分析。统计数据如下表7:表75个杂优水稻品种干物质积累资料重复I5n12345品种1234A11.410.59.910.1B8.1C12.610.211.411.812.312.51

6、2.9D7.9E13.815.113.412.616.611.717.215.615.115.8Double （4）两因素完全随机试验的方差分析例1、为了研究不同的田间管理方法对草莓产量的影响，选择了 个不同的地块，每个地块分成3个小区，随机安排3种田间管理方法， 所得结果见下表1,进行方差分析。（两因素交叉分组单个观察值试验 资料）。表1各地块不同管理措施的草莓产量A717377A909092A597080A758082A656067A828685田间管理方法（B）地块（A）B1（化学控制）B2 （集成虫害管理）R （改良集成虫害管理）例

7、2、某毛纺织厂为了研究毛纱与股线在选取不同捻度时对某种毛 织物强力的影响，特选用了表2.1的因素水平。（多个观察值试验资料）表2.1 2因素3水平捻度表单位：捻/米捻度水平 因素、123A:毛纱捻度460530600B:股线捻度460530600按照以上不同捻度水平的毛纱、股线经织造与后整理，然后对该毛织物做强力试验，测得强力值数据如表1.2所示（每个方案下共试验 3次）。表2.2 毛织物强力测试数据表单位：Kg处 理测试数据Bl616261aB2606162B3616161B606061aB2605961B3626061B606062aB2636463B3606061两因素随机区组试验的方差

8、分析例3、将水稻的3个不同细胞质源的不育系（Ai、A2、A3）和5 个恢复系（Bi、B2、B3、B4、B5）杂交，配成15个Fi。采用随机区组设 计，重复2次，小区计产面积6m2。小区稻谷产量（公斤）列于下表3。试作分析。表3水稻杂交小区稻谷产量资料处理-区组InB14.34.1B4.94.8a&3.93.6B44.84.0&4.74.5B15.24.7B25.05.2aB33.83.4B44.94.8&5.05.8B14.64.7B4.44.2aB33.53.4B43.43.6B53.74.2例4、为了研究不同的种植密度和商业化肥对大麦产量的影响，将种植密度（A）设置

9、3个水平，施用的商业化肥（B）设置5个水平，交叉分组，重复4次，完全随机设计。产量结果（Kg/小区）列于下表4,分析种植密度和施用的商业化肥对大麦产量的影响。（两因素交叉分组有重复观察值试验）。表4、不同种植密度和商业化肥的大麦试验的产量结果（Kg/小区）A2A3BB2B3BB5272631302529253030252624303126262931302430283132283027313429282630332829253232273333353530333433342934343733313235353530Triple （3）三因素随机区组试验的方差分析棉两个水平;例1、有一棉花栽培试

10、验，A因素为品种，有 A1=陆地棉，A2=草C因素B因素为播期，B1=谷雨播，B2=立夏播两个水平；为密度，G=3500株/亩，C2=7000株/亩，C3=10500株/亩三个水平。随机区组设计，重复 3次，小区计产面积 40m2。表1各处理对应小区产量资料（Kg）处理-区组InrnC1121413BC2121111C31099AC11099RC2998C3667C1324C2434C3767AC1223C2345C3577例2、有一养麦品种抗旱性和耐热性试验，A因素为品种，Ai=美国养麦，A2二通选90养麦，A3=蒙87养麦，£=大黑三棱养麦；B因素为时间（种子处理：取饱满发芽力强

11、的四种养麦种子分别放于室温中浸润吸水，然后放于温箱中25 C下发芽，芽长1cm时取出分别进行干处理的时间），Bi=18小时，理完在分别进行热处理B2=24小时，B3=48小时；C因素为温度（干处1小时）,G=36C, C2=38C。然后经干旱和热处理的发芽种子，用刀片切下根尖23mm ,用碘液染色，放于显微镜F观察各个不同温度、时间的根尖各10个统计的根管淀粉水解粒数。其淀粉水解率表如下:表2养麦品种淀粉水解率表处理水解率（%BCi68C273AE2Ci78C293BbCi87C293BCi57C261AE2CiC27178E3Ci80C288BCi37C241AE2CiC25561E3C16

12、6C277BG70C275AE2C182C286E3C191C298例3、大豆异黄酮和皂苷试大豆中的主要次生代谢物质，二者都具有许多生理活性功能，如防癌抗癌、防心血管病等功能，本研究以20个不同类型的大豆品种为基础材料，在2个年份里分9个播期种植，共收获360份大豆样品。测定了全部样品的异黄酮和皂苷含量，试分析年份、播期和品种对异黄酮和皂苷含量的影响程度。A因素为年份，Ai=2004年，A2=2OO5年；B因素为品种，Bi二南春201，B2=武昌六月爆，号,B3=筠连九转豆，B4=a豆3号，B5=V97-5391，B6=扇子白，B7=巴马九月 黄，B8=启东羊眼豆，B9二冀豆10号，B1o=安

13、吉青豆，B11= PI548662,B12=J280082，B13=493-1，B14=淳平小子药黑豆，B15=SU-123, B16=早踏B19=桂阳紫金豆，B2O=如东晚绿黄；C扁青，B17=奥莱，B18=黑豆一号，因素为播期，G=3月15日，C2=4月15日，C3=5月15日，Q=6月15 日，G=7月15日，C6=8月15日。（2005年只在C2、C4、 C6三期播种。）按以上方法对360份大豆样品中的异黄酮含量进行测定，结果统 计于下表3.1和表3.2。（1）、试分析品种和播期对大豆成熟籽粒中异黄酮含量的影响;（从表可以看出，各品种在播期相同的情况下，大豆籽粒异黄酮含量 有差异，而同

14、一品种在播期不同的情况下也有差异，对品种和播期作因素分析。）（2）、试分析年份、品种和播期对大豆成熟籽粒中异黄酮含量的影响。（可将2004年4月（G）、6月（C4）、8月（C6）各品种所对应 的异黄酮含量值与 2005年4月（C2）、6月（C4）、8月（C6）各品种所表3.12004年各播期大豆籽粒总异黄酮积累量（卩g/g ）Table3.1 Soybea n isoflav ones accumulati on qua ntity of every sow ing time in 2004B:品种名称 _C:播 期（sowing time )(variety)C(Mar.15th)C2(Ap

15、 r.15th)G(May.15th)C4(Jun .15th)G(Jul.15th)G(Aug.15th)南春2011283.091378.18683.591508.202176.063430.08武昌六月爆1484.65836.551423.211897.942248.493236.27筠连九转豆668.58741.241117.192405.412963.952840.79通豆3号1939.452104.132365.352518.473099.272944.75V97-53911229.521600.951867.412661.333558.093579.35扇子白1961.33212

16、5.782117.802508.763049.673030.36巴马九月黄1772.882029.192124.112333.262433.312637.33启东羊眼豆1310.441281.471316.351543.751817.632275.84冀豆10号749.22617.75933.482190.793378.074564.56安吉青豆1700.001920.702137.611940.682760.102446.71PI5486632663.172920.652800.673007.313515.402993.02J2800822542.022721.602896.373494.7

17、53919.143529.69493-11220.591472.491709.152493.693183.932933.48淳平小子药黑豆1283.82762.781304.801990.632360.442804.80SU-123539.96728.351130.971921.372364.683524.33早踏扁青886.381160.831400.951762.442652.062454.63奥莱355.69403.68574.001489.561327.092515.46黑豆一号1378.13630.58372.381095.311870.093580.86桂阳紫金豆1204.8596

18、2.501660.832380.362974.113826.84如东晚绿黄2481.532597.772576.623339.513639.292653.07表3.22005年各播期大豆籽粒总异黄酮积累量（卩g/g ）Table3.1 Soybea n isoflav ones accumulati on qua ntity of every sow ing time in 2005B:品种名称(variety)C:播期(sowing time )G(A pr.15th)C4(J un .15th)C6(Aug.15th)南春201747.661300.733186.16武昌六月爆1249.5

19、51535.943525.17筠连九转豆652.291494.482980.69通豆3号1200.892423.443510.49V97-5391751.282556.033048.49扇子白1749.162284.042875.06巴马九月黄1329.072024.332862.83启东羊眼豆826.061257.032379.41冀豆10号643.581326.624507.76安吉青豆1343.302070.543473.88PI5486632054.412463.282687.56J2800821256.862509.653449.11493-11044.871611.723878.6

20、3淳平小子药黑豆833.431147.662687.22SU-123659.321354.132823.10早踏扁青663.561450.842791.74奥莱255.971158.541931.03黑豆一号832.42680.193158.37桂阳紫金豆1463.842380.363590.57如东晚绿黄1782.092241.963352.23Single (7)Case 1 China agricultural uni versity in troduced 15 type of Trestorer. I n order to study the app licati on value,

21、 we observed their rep rese ntati on of agrono mic characters, among these non gda139 isCK. The results of the headi ng stage of 5 plants are show n in table1.Table 1 The results of the headi ng stage of 5 plantsRestorerHeadi ng stage12345PI2770161111101211Lot-11313121414Texas1212131212zgR2806-78131

22、2121313zgR2268-781819181819vk-64-281918201919Nongda 1391011101110Case 2 Do a po tted exp erime nt about 5 varieties of corn, thecharacter of spike length are shown in table 2. Ask whether the differe nee betwee n sp ike len gth sig nifica nee or not.Table 2 The results of the character of sp ike len

23、 gthVarietiesSp ike len gth(cm)Rep eatsB121.519.5202218206B21618.51715.520166B31917.52018175B42118.519204B515.51817164Case 3 The weight of pi glet in the test cross ing betwee n the same boar and 3 sows are show n in the table 3. Ask whether the differe nt sows bring the differe nt effects of pi gle

24、t weight or not.No.12422.5242022232222.5No.21919.52023.5192116.5No.3161615.520.51417.514.515.5 19SowsObserved valuesTable 3 The weight of pi gletCase 4 Comparative study on the yield of different rice varieties by ran domized blocks desig n method. There are 4 rep eats. The yields of every block are

25、 shown in table 4. Try analyze whether the differe nee among 5 rice varieties sig nifica nt or not.Table 4 The yields of every blockVarietiesBlocksInmIVNo nglinihai 6753525051Shishi52585557Non gli n 8758565353Non gli n 1853515455Case 5 We soak a soybea n variety in three time p eriods b

26、y growth horm one in 5 levels. After 45 days, average dry weight ofevery treatme nt is show n in table 5. Try doing varia nee an alysis.Table 5 Effects of growth horm one on soybea n dry weightMi(Growth hormone )Hi (Time periods )HiH2H3Mi131414M2121213M3333M410910M5254Case 6 In order to study parent

27、 gen eral comb ining ability,China agricultural uni versity desig n 4X5 crosses exp erime nt by ran domized blocks desig n method. There are 3 rep eats, andNongda 139 is CK. The parts of the grain number per spike material are show n in table 6.Table 6 The p arts of the grain nu mber per sp ike mate

28、rialxRe peatsInrnCrosses12345123451234511516171516151515161515141516162151516151515151415161514151616314141513141616141615161415151641516161516151615161515171714155161717171716171817171819171718Non gda 139141413121213131212121212141313Case7OnA,B,C,D,E5hybridrice (drymaitteraccumulation process were

29、tested systematically. We adoptran domized blocks desig n, 2 rep eats,a nd 5 observed values. Try doing varia nee an alysisStatistical data are give n in Table 7.Table 7 Dry matter accumulati on materialRep eatsInVarieties1234512345A11.410.59.910.1B8.1C

30、12.610.211.411.812.312.512.9D7.9E13.815.113.412.616.611.717.215.615.115.8Double (4)Case 1 In order to study the effects of different field man ageme nts to the yield of strawberry, we select 6 differe nt plots,and divide it into 3 blocks arranged by 3 kinds of

31、field man ageme nts ran domly. The yield of strawberry in differe nt blocks are show n in table 1.Try doing varia nee an alysis.Table 1 The yield of strawberry in differe nt blocksField man ageme nts(B)Plots (A)B1(ChemicalB2 (IntegratedB3 (Im proved in tegratedcon trol)man ageme nt of p est)man agem

32、e nt of p est)A1717377A2909092A3597080A4758082A5656067A6828685Case 2 In order to study the effects on different degree of entwist to the mightiness of some aba, we choose the different levels in some factors, the entwist degree of caddice(A) andthigh(B) as shown in table 2.1 and the observed value o

33、f mighti ness are show n in table 2.2.Table 2.1 Two factors, three levelsLevelsFactors123A460530600B460530600Table 2.2 The observed value of might in essTreatme ntsObserved valuesB1616261A1B2606162B3616161B1606061A2B2605961B3626061B1606062A3B2636463B3606061Case 3 We crossing sterility lines（Ai、A2、A3

34、） of 3 different cyt op lasmic and 5 restorer lin esBi、B2、B3、B4、B5）, the n matchi ng 15 F1 gen erati ons by ran domized blocks desig n and 2 rep eats. The2yields of blocks in 6m are shown in table 3.Table 3 The yield of p addy in 6 m2Treatme ntsRep eatsInB14.34.1B24.94.8A1B33.93.6B44.84.0B54.74.5B15

35、.24.7B25.05.2A2B33.83.4B44.94.8B55.05.8B14.64.7B24.44.2A3B33.53.4B43.43.6B53.74.2Case 4 The exp erime nt studied the relati onship betwee n the yield of barley and different sowing densities, and commercial fertilizer by random complete design. Sowing density were set 3 levels, and commercial fertil

36、izer were set 5 levels, in tercross grouping, rep eat 4 times. The results of differe nt group are list in table 4.Table 4 The yield of the result of differe nt groupB1B2B3B4B52726313025A12925303025262430312626293130243028313228A23027313429282630332829253232273333353530A33334333429343437333132353535

37、30Triple (3)Case 1 The exp erime nt studied the relati on shi p betwee n the yield of cott on and other factors by ran domized blocks desig n. Factor A is variety, A1 is upland cott on; A2 is Leva nt cott on. Factor B is sowi ng time, B1 is sowi ng in Grain rai n; B2 is sowi ng in Summer begins. Fac

38、tor C is density, C1 is 3500 plants each 666.7m ; C2 is 7000 p la nts each 666.7& C3 is 10500. The area of yield is 40m2, rep eats 3 times. The results of each treatme nt are list in the table 1.Table 1 The yield of each treatme ntTreatme nts-BlocksInmC1121413B1C2121111C31099A1C11099B2C2998C3667

39、C1324B1C2434C3767A2C1223B2C2345C3577Case 2 The exp erime nt studied on the drought resista nt and heat resista nceof some buckwheat. Factor A is variety, A 1 is America buckwheat; A2 is Tongxuan90 buckwheat; A3 is Meng87 buckwheat; A4 is Daheisanieng buckwheat. Factor B is period of time of treatmen

40、t, B 1 is 18 hours; B 2 is 24 hours; B 3 is 48 hours.Factor C is temperature of heat treatment about one hours, C1 is 36C ; C2 is 38 C . After the treatment of drought and heat, we cut dow n root tip 23mm of the germ in at ing seed, and the n sta ining it with iodi ne soluti on and calculati ng the

41、hydrolysis of starch grain number. The hydrolyze rate of buckwheat of different treatmentsare list in table 2：Table 2 The hydrolyze rate of buckwheat of differe nt treatme ntsTreatme ntsHydrolyze rate (%)BiC168C273B2C178A1C293BsC187C293BiC157C261B2C171AC278C180B3C288BiC137C241C155AsB2C261BsC166C277C

42、170BiC275C182A4B2C286C191BsC298Case 3 Soybean isoflavone and Soyasaponins are main sec on dary metabolite matter of soybea n. The two all has many biological activity fun cti ons, such as curi ng and p reve nting can cer and cardiovascular disease and the like. In this exp erime nt, 20 differe nt ty

43、pe soybea n varieties are selected as the research object.There are 9 seed-times to plant in two year stabs, and 360 soybea ns samp les are harvested altogether. The content of Soybea n isoflav one and Soyasa ponin is determ ined for all samp les.Comparing the degree of the in flue nee effect about

44、varietySow ing time and year factors for Soybean isoflavones and Soyasaponin content. Factor A is year, A1 is the year of 2004; A 2 is the year of 2005. Factor B is varieties, B1 is Nanchun201; B2 isWucha ngliuyuebao; B3 is Jun lia njiuzhua ndou; B4 is Ton gdouNo.3;B5 is V97-5391; B6 is Shanzibai; B

45、? is Bamaliuyuehuang; B8 isQidon gya ngya ndou; B9 is JidouNo.10; B10 is Anjieq in gdou; B 11 isPI548662; B12 is J280082;B13is 493-1; B14 isChunpingxiaoziyaoheidou; B15 is SU-123; B16 is Zaotabianqing;Bi7 is Aolai; B18 is HeidouNo.1; B19 is Guiyangzijindou; B20 isRudongwanlvhuang; Factor C is sowing

46、 time, C 1 is Mar.15; C 2 isApr.15; C3 is May 15; C 4 is Jun 15; C5 is Jul.15; C6 is Aug.15.(ln 2005,we just sowing soybean in C1、C2 and C3.) Then, we determ ined the content of Soybea n isoflav one and Soyasa ponin for 360 soybea ns samp les, the results are list in table 3.1 and 3.2.(1)、Try an alyze the degree of the in flue nee effect aboutvariety and sow ing time for Soybea n isof