ANOVA分析例題

1、Single（ 7）單因素單向分組方差分析例1、北京農業(yè)大學從南斯拉夫引進15個T型恢復材料，為了研究其應用價值，以農大139為對照，進行了個農藝性狀表現的觀察。其中6個恢復材料和農大139各5個單株抽穗期觀察結果如表1 :引進恢復系抽穗期觀察資料恢復系-單株抽穗期12345PI2770161111101211Lot-11313121414Texas1212131212zgR2806-781312121313zgR2268-781819181819vk-64-281918201919農大1391011101110例2、5個玉米品種的盆栽試驗，調查了穗長（ cm）性狀，得資2，試檢驗品種穗長間有

2、無差異。（各處理的重復數不等）表25個玉米品種的穗長B121.519.5202218206B21618.51715.520166B31917.520181752118.519204B515.51817164品種穗長（cm）重復數例3、表3為同一公豬配種的3頭母豬所產的各頭仔豬的斷奶時（每組樣本容體重（斤），試分析母豬對仔豬體重效應的差異顯著性。量不等）表3二頭母豬的仔豬斷奶時體重母豬別ni觀察值No.182422.5242022232222.5No.271919.52023.5192116.5No.39161615.520.51417.514.515.519單因素雙向分組方差分析小區(qū)內沒有重復

3、觀察值例4、5個水稻品種的產量比較試驗，隨機區(qū)組設計，4次重復，獲得每個小區(qū)產量（Kg）資料如表4所示：試分析這 5個水稻品種間產量水平有無顯著差異。表4水稻5個品種的每區(qū)產量（Kg）例5、將一種生長激素配成 M1、M2、M 3、IVI4、M4、M5五種濃度，并用Hl、H2、H3、種時間浸漬某大豆品種的種子，45天后得各處理每口礎區(qū)組（重復）InrnIV農海6753525051十石52585557農林8758565353農林1853515455植株的平均干物重（g）于下表5,試作方差分析。表5生長激素對大豆干重的影響M（生長激素）H （時間）HHbM1131414M2

4、121213M3333M410910M5254小區(qū)內有重復觀察值例6、北京農業(yè)大學以4X 5的兩個親本雜交設計研究親本配合力，隨機區(qū)組設計 3次重復，從樣段內隨機抽取 10株進行考種，其5個組合和對照農大 139的結實小穗數部分資料如下表6:（部分是指其中5個組合+CK 3次重復，每小區(qū)5株的考種數據。）表6兩組親本雜交結實小穗數部分資料重復&合In123451234512345115161715161515151615151415161621515161515151514151615141516163141415131416161416151614151516415161615161

5、51615161515171714155161717171716171817171819171718農大139141413121213131212121212141313例7、對A、B、C、D、E 5個雜優(yōu)水稻品種的干物質積累過程進行了系統(tǒng)的測定，隨機區(qū)組設計，2次重復，每小區(qū)5株觀察數據。試作方差分析。統(tǒng)計數據如下表7:表75個雜優(yōu)水稻品種干物質積累資料重復I5n12345品種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）兩因素完全隨機試驗的方差分析例1、為了研究不同的田間管理方法對草莓產量的影響，選擇了 個不同的地塊，每個地塊分成3個小區(qū)，隨機安排3種田間管理方法， 所得結果見下表1,進行方差分析。（兩因素交叉分組單個觀察值試驗 資料）。表1各地塊不同管理措施的草莓產量A717377A909092A597080A758082A656067A828685田間管理方法（B）地塊（A）B1（化學控制）B2 （集成蟲害管理）R （改良集成蟲害管理）例

7、2、某毛紡織廠為了研究毛紗與股線在選取不同捻度時對某種毛 織物強力的影響，特選用了表2.1的因素水平。（多個觀察值試驗資料）表2.1 2因素3水平捻度表單位：捻/米捻度水平 因素、123A:毛紗捻度460530600B:股線捻度460530600按照以上不同捻度水平的毛紗、股線經織造與后整理，然后對該毛織物做強力試驗，測得強力值數據如表1.2所示（每個方案下共試驗 3次）。表2.2 毛織物強力測試數據表單位：Kg處 理測試數據Bl616261aB2606162B3616161B606061aB2605961B3626061B606062aB2636463B3606061兩因素隨機區(qū)組試驗的方差

8、分析例3、將水稻的3個不同細胞質源的不育系（Ai、A2、A3）和5 個恢復系（Bi、B2、B3、B4、B5）雜交，配成15個Fi。采用隨機區(qū)組設 計，重復2次，小區(qū)計產面積6m2。小區(qū)稻谷產量（公斤）列于下表3。試作分析。表3水稻雜交小區(qū)稻谷產量資料處理-區(qū)組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、為了研究不同的種植密度和商業(yè)化肥對大麥產量的影響，將種植密度（A）設置

9、3個水平，施用的商業(yè)化肥（B）設置5個水平，交叉分組，重復4次，完全隨機設計。產量結果（Kg/小區(qū)）列于下表4,分析種植密度和施用的商業(yè)化肥對大麥產量的影響。（兩因素交叉分組有重復觀察值試驗）。表4、不同種植密度和商業(yè)化肥的大麥試驗的產量結果（Kg/小區(qū)）A2A3BB2B3BB5272631302529253030252624303126262931302430283132283027313429282630332829253232273333353530333433342934343733313235353530Triple （3）三因素隨機區(qū)組試驗的方差分析棉兩個水平;例1、有一棉花栽培試

10、驗，A因素為品種，有 A1=陸地棉，A2=草C因素B因素為播期，B1=谷雨播，B2=立夏播兩個水平；為密度，G=3500株/畝，C2=7000株/畝，C3=10500株/畝三個水平。隨機區(qū)組設計，重復 3次，小區(qū)計產面積 40m2。表1各處理對應小區(qū)產量資料（Kg）處理-區(qū)組InrnC1121413BC2121111C31099AC11099RC2998C3667C1324C2434C3767AC1223C2345C3577例2、有一養(yǎng)麥品種抗旱性和耐熱性試驗，A因素為品種，Ai=美國養(yǎng)麥，A2二通選90養(yǎng)麥，A3=蒙87養(yǎng)麥，£=大黑三棱養(yǎng)麥；B因素為時間（種子處理：取飽滿發(fā)芽力強

11、的四種養(yǎng)麥種子分別放于室溫中浸潤吸水，然后放于溫箱中25 C下發(fā)芽，芽長1cm時取出分別進行干處理的時間），Bi=18小時，理完在分別進行熱處理B2=24小時，B3=48小時；C因素為溫度（干處1小時）,G=36C, C2=38C。然后經干旱和熱處理的發(fā)芽種子，用刀片切下根尖23mm ,用碘液染色，放于顯微鏡F觀察各個不同溫度、時間的根尖各10個統(tǒng)計的根管淀粉水解粒數。其淀粉水解率表如下:表2養(yǎng)麥品種淀粉水解率表處理水解率（%BCi68C273AE2Ci78C293BbCi87C293BCi57C261AE2CiC27178E3Ci80C288BCi37C241AE2CiC25561E3C16

12、6C277BG70C275AE2C182C286E3C191C298例3、大豆異黃酮和皂苷試大豆中的主要次生代謝物質，二者都具有許多生理活性功能，如防癌抗癌、防心血管病等功能，本研究以20個不同類型的大豆品種為基礎材料，在2個年份里分9個播期種植，共收獲360份大豆樣品。測定了全部樣品的異黃酮和皂苷含量，試分析年份、播期和品種對異黃酮和皂苷含量的影響程度。A因素為年份，Ai=2004年，A2=2OO5年；B因素為品種，Bi二南春201，B2=武昌六月爆，號,B3=筠連九轉豆，B4=a豆3號，B5=V97-5391，B6=扇子白，B7=巴馬九月 黃，B8=啟東羊眼豆，B9二冀豆10號，B1o=安

13、吉青豆，B11= PI548662,B12=J280082，B13=493-1，B14=淳平小子藥黑豆，B15=SU-123, B16=早踏B19=桂陽紫金豆，B2O=如東晚綠黃；C扁青，B17=奧萊，B18=黑豆一號，因素為播期，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、 C6三期播種。）按以上方法對360份大豆樣品中的異黃酮含量進行測定，結果統(tǒng) 計于下表3.1和表3.2。（1）、試分析品種和播期對大豆成熟籽粒中異黃酮含量的影響;（從表可以看出，各品種在播期相同的情況下，大豆籽粒異黃酮含量 有差異，而同

14、一品種在播期不同的情況下也有差異，對品種和播期作因素分析。）（2）、試分析年份、品種和播期對大豆成熟籽粒中異黃酮含量的影響。（可將2004年4月（G）、6月（C4）、8月（C6）各品種所對應 的異黃酮含量值與 2005年4月（C2）、6月（C4）、8月（C6）各品種所表3.12004年各播期大豆籽?？偖慄S酮積累量（卩g/g ）Table3.1 Soybea n isoflav ones accumulati on qua ntity of every sow ing time in 2004B:品種名稱 _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筠連九轉豆668.58741.241117.192405.412963.952840.79通豆3號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巴馬九月黃1772.882029.192124.112333.262433.312637.33啟東羊眼豆1310.441281.471316.351543.751817.632275.84冀豆10號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淳平小子藥黑豆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奧萊355.69403.68574.001489.561327.092515.46黑豆一號1378.13630.58372.381095.311870.093580.86桂陽紫金豆1204.8596

18、2.501660.832380.362974.113826.84如東晚綠黃2481.532597.772576.623339.513639.292653.07表3.22005年各播期大豆籽粒總異黃酮積累量（卩g/g ）Table3.1 Soybea n isoflav ones accumulati on qua ntity of every sow ing time in 2005B:品種名稱(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筠連九轉豆652.291494.482980.69通豆3號1200.892423.443510.49V97-5391751.282556.033048.49扇子白1749.162284.042875.06巴馬九月黃1329.072024.332862.83啟東羊眼豆826.061257.032379.41冀豆10號643.581326.624507.76安吉青豆1343.302070.543473.88PI5486632054.412463.282687.56J2800821256.862509.653449.11493-11044.871611.723878.6

20、3淳平小子藥黑豆833.431147.662687.22SU-123659.321354.132823.10早踏扁青663.561450.842791.74奧萊255.971158.541931.03黑豆一號832.42680.193158.37桂陽紫金豆1463.842380.363590.57如東晚綠黃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