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：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，得資料如下表2，試檢驗品種

2、穗長間有無差異。（各處理的重復數不等）表2 5個玉米品種的穗長品種穗長（cm）重復數B121.519.5202218206B21618.51715.520166B31917.52018175B42118.519204B515.51817164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體重（斤），試分析母豬對仔豬體重效應的差異顯著性。（每組樣本容量不等）表3 三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

3、析小區(qū)內沒有重復觀察值 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）品種區(qū)組（重復）農海6753525051十石52585557農林8758565353農林1853515455 例5、將一種生長激素配成M1、M2、M3、M4、M5五種濃度，并用H1、H2、H3、三種時間浸漬某大豆品種的種子，45天后得各處理每一植株的平均干物重（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Mi（生長激素）Hi（時間）H1H2H3M11314

4、14M2121213M3333M410910M5254小區(qū)內有重復觀察值 例6、北京農業(yè)大學以4×5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，其中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 組合123451234512345115161715161515151615151415161621515161515151514151615141516163141415131416161416151614151516415161615

5、16151615161515171714155161717171716171817171819171718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7 5個雜優(yōu)水稻品種干物質積累資料重復 品種1234512345A7.88.99.211.410.512.110.68.79.910.1B7.48.88.97.89.86.26.65.37.58.1C12.610.211.411.812.115.215.112.312

6、.512.9D5.84.76.67.47.96.46.88.17.27.9E13.815.113.412.616.611.717.215.615.115.8Double（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6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地塊（A）田間管理方法（B）B1(化學控制)B2（集成蟲害管理）B3（改良集成蟲害管理）A1717377A2909092A3597080A4758082A5656067A68

7、28685例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A1B1616261B2606162B3616161A2B1606061B2605961B3626061A3B1606062B2636463B3606061

8、兩因素隨機區(qū)組試驗的方差分析例3、將水稻的3個不同細胞質源的不育系（A1、A2、A3）和5個恢復系（B1、B2、B3、B4、B5）雜交，配成15個F1。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A1B14.34.1B24.94.8B33.93.6B44.84.0B54.74.5A2B15.24.7B25.05.2B33.83.4B44.94.8B55.05.8A3B14.64.7B24.44.2B33.53.4B43.43.6B53.74.2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（

9、A）設置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)）B1B2B3B4B5A12726313025292530302526243031262629313024A23028313228302731342928263033282925323227A33333353530333433342934343733313235353530Triple（3）三因素隨機區(qū)組試驗的方差分析例1、有一棉花栽

10、培試驗，A因素為品種，有A1=陸地棉，A2=草棉兩個水平；B因素為播期，B1=谷雨播，B2=立夏播兩個水平；C因素為密度，C1=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A1B1C1121413C2121111C31099B2C11099C2998C3667A2B1C1324C2434C3767B2C1223C2345C3577例2、有一蕎麥品種抗旱性和耐熱性試驗，A因素為品種，A1=美國蕎麥，A2=通選90蕎麥，A3=蒙87蕎麥，A4=大黑三棱蕎麥；B因素為時間（種子處

11、理：取飽滿發(fā)芽力強的四種蕎麥種子分別放于室溫中浸潤吸水，然后放于溫箱中25下發(fā)芽，芽長1cm時取出分別進行干處理的時間），B1=18小時，B2=24小時，B3=48小時；C因素為溫度（干處理完在分別進行熱處理1小時），C1=36，C2=38。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，放于顯微鏡下觀察各個不同溫度、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 蕎麥品種淀粉水解率表處 理水解率（%）A1B1C168C273B2C178C293B3C187C293A2B1C157C261B2C171C278B3C180C288A3B1C137C241B2

12、C155C261B3C166C277A4B1C170C275B2C182C286B3C191C298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，A1=2004年，A2=2005年；B因素為品種，B1=南春201，B2=武昌六月爆，B3=筠連九轉豆，B4=通豆3號，B5=V97-5391，B6=扇子白，B7=巴馬九月黃，B8=啟東羊眼豆，B

13、9=冀豆10號，B10=安吉青豆，B11=PI548662，B12=J280082，B13=493-1，B14=淳平小子藥黑豆，B15=SU-123，B16=早踏扁青，B17=奧萊，B18=黑豆一號，B19=桂陽紫金豆，B20=如東晚綠黃； C因素為播期，C1=3月15日，C2=4月15日，C3=5月15日，C4=6月15日，C5=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

14、籽粒異黃酮含量有差異，而同一品種在播期不同的情況下也有差異，對品種和播期作二因素分析。）（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（C2）、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）各品種所對應的異黃酮含量值組成三因素方差分析表。）表3.1 2004年各播期大豆籽?？偖慄S酮積累量（µg/g）Table3.1 Soybean isoflavones accumulation quantity of every sowing time in 2004B:品種名稱(variety)C:播

15、 期（sowing time）C1 (Mar.15th)C2 (Apr.15th)C3 (May.15th)C4 (Jun.15th)C5 (Jul.15th)C6 (Aug.15th)南春2011283.09 1378.18 683.59 1508.20 2176.06 3430.08 武昌六月爆1484.65 836.55 1423.21 1897.94 2248.49 3236.27 筠連九轉豆668.58 741.24 1117.19 2405.41 2963.95 2840.79 通豆3號1939.45 2104.13 2365.35 2518.47 3099.27 2944.75

16、V97-53911229.52 1600.95 1867.41 2661.33 3558.09 3579.35 扇子白1961.33 2125.78 2117.80 2508.76 3049.67 3030.36 巴馬九月黃1772.88 2029.19 2124.11 2333.26 2433.31 2637.33 啟東羊眼豆1310.44 1281.47 1316.35 1543.75 1817.63 2275.84 冀豆10號749.22 617.75 933.48 2190.79 3378.07 4564.56 安吉青豆1700.00 1920.70 2137.61 1940.68 2

17、760.10 2446.71 PI5486632663.17 2920.65 2800.67 3007.31 3515.40 2993.02 J2800822542.02 2721.60 2896.37 3494.75 3919.14 3529.69 493-11220.59 1472.49 1709.15 2493.69 3183.93 2933.48 淳平小子藥黑豆1283.82 762.78 1304.80 1990.63 2360.44 2804.80 SU-123539.96 728.35 1130.97 1921.37 2364.68 3524.33 早踏扁青886.38 1160

18、.83 1400.95 1762.44 2652.06 2454.63 奧萊355.69 403.68 574.00 1489.56 1327.09 2515.46 黑豆一號1378.13 630.58 372.38 1095.31 1870.09 3580.86 桂陽紫金豆1204.85 962.50 1660.83 2380.36 2974.11 3826.84 如東晚綠黃2481.53 2597.77 2576.62 3339.51 3639.29 2653.07 表3.2 2005年各播期大豆籽?？偖慄S酮積累量（µg/g）Table3.1 Soybean isoflavone

19、s accumulation quantity of every sowing time in 2005B:品種名稱(variety)C:播 期（sowing time）C2(Apr.15th)C4(Jun.15th)C6(Aug.15th)南春201747.66 1300.73 3186.16 武昌六月爆1249.55 1535.94 3525.17 筠連九轉豆652.29 1494.48 2980.69 通豆3號1200.89 2423.44 3510.49 V97-5391751.28 2556.03 3048.49 扇子白1749.16 2284.04 2875.06 巴馬九月黃132

20、9.07 2024.33 2862.83 啟東羊眼豆826.06 1257.03 2379.41 冀豆10號643.58 1326.62 4507.76 安吉青豆1343.30 2070.54 3473.88 PI5486632054.41 2463.28 2687.56 J2800821256.86 2509.65 3449.11 493-11044.87 1611.72 3878.63 淳平小子藥黑豆833.43 1147.66 2687.22 SU-123659.32 1354.13 2823.10 早踏扁青663.56 1450.84 2791.74 奧萊255.97 1158.54

21、1931.03 黑豆一號832.42 680.19 3158.37 桂陽紫金豆1463.84 2380.36 3590.57 如東晚綠黃1782.09 2241.96 3352.23 Single（7）Case 1 China agricultural university introduced 15 type of T restorer. In order to study the application value, we observed their representation of agronomic characters, among these nongda139 is CK.

22、The results of the heading stage of 5 plants are shown in table 1.Table 1 The results of the heading stage of 5 plantsRestorerHeading stage 12345PI2770161111101211Lot-11313121414Texas1212131212zgR2806-781312121313zgR2268-781819181819vk-64-281918201919Nongda 1391011101110Case 2 Do a potted experiment

23、 about 5 varieties of corn, the character of spike length are shown in table 2. Ask whether the difference between spike length significance or not.Table 2 The results of the character of spike lengthVarietiesSpike length（cm）RepeatsB121.519.5202218206B21618.51715.520166B31917.52018175B42118.519204B5

24、15.51817164Case 3 The weight of piglet in the test crossing between the same boar and 3 sows are shown in the table 3. Ask whether the different sows bring the different effects of piglet weight or not. Table 3 The weight of pigletSowsObserved valuesNo.12422.5242022232222.5No.21919.52023.5192116.5No

25、.3161615.520.51417.514.515.519Case 4 Comparative study on the yield of different rice varieties by randomized blocks design method. There are 4 repeats. The yields of every block are shown in table 4. Try analyze whether the difference among 5 rice varieties significant or not. Table 4 The yields of

26、 every blockVarietiesBlocksNonglinihai 6753525051Shishi52585557Nonglin 8758565353Nonglin 1853515455Case 5 We soak a soybean variety in three time periods by growth hormone in 5 levels. After 45 days, average dry weight of every treatment is shown in table 5. Try doing variance analysis.

27、 Table 5 Effects of growth hormone on soybean dry weightMi（Growth hormone）Hi（Time periods）H1H2H3M1131414M2121213M3333M410910M5254Case 6 In order to study parent general combining ability, China agricultural university design 4×5 crosses experiment by randomized blocks design method. There are 3

28、 repeats, and Nongda 139 is CK. The parts of the grain number per spike material are shown in table 6.Table 6 The parts of the grain number per spike materialRepeatsCrosses12345123451234511516171516151515161515141516162151516151515151415161514151616314141513141616141615161415151641516161516151615161

29、515171714155161717171716171817171819171718Nongda 139141413121213131212121212141313Case 7 On A, B, C, D, E 5 hybrid rice dry matter accumulation process were tested systematically. We adopt randomized blocks design, 2 repeats, and 5 observed values. Try doing variance analysis. Statistical data are g

30、iven in Table 7.Table 7 Dry matter accumulation materialRepeats Varieties1234512345A7.88.99.211.410.512.110.68.79.910.1B7.48.88.97.89.86.26.65.37.58.1C12.610.211.411.812.115.215.112.312.512.9D5.84.76.67.47.96.46.88.17.27.9E13.815.113.412.616.611.717.215.615.115.8Double（4）Case 1 In order to study the

31、 effects of different field managements to the yield of strawberry, we select 6 different plots, and divide it into 3 blocks arranged by 3 kinds of field managements randomly. The yield of strawberry in different blocks are shown in table 1.Try doing variance analysis.Table 1 The yield of strawberry

32、 in different blocksPlots（A）Field managements（B）B1(Chemical control)B2（Integrated management of pest）B3（Improved integrated management of pest）A1717377A2909092A3597080A4758082A5656067A6828685Case 2 In order to study the effects on different degree of entwist to the mightiness of some aba, we choose

33、the different levels in some factors, the entwist degree of caddice(A) and thigh(B) as shown in table 2.1 and the observed value of mightiness are shown in table 2.2.Table 2.1 Two factors, three levels LevelsFactors123A 460530600B 460530600Table 2.2 The observed value of mightinessTreatmentsObserved

34、 valuesA1B1616261B2606162B3616161A2B1606061B2605961B3626061A3B1606062B2636463B3606061Case 3 We crossing sterility lines(A1、A2、A3) of 3 different cytoplasmic and 5 restorer lines(B1、B2、B3、B4、B5), then matching 15 F1 generations by randomized blocks design and 2 repeats. The yields of blocks in 6m2 ar

35、e shown in table 3.Table 3 The yield of paddy in 6m2TreatmentsRepeatsA1B14.34.1B24.94.8B33.93.6B44.84.0B54.74.5A2B15.24.7B25.05.2B33.83.4B44.94.8B55.05.8A3B14.64.7B24.44.2B33.53.4B43.43.6B53.74.2Case 4 The experiment studied the relationship between the yield of barley and different sowing densities

36、, and commercial fertilizer by random complete design. Sowing density were set 3 levels, and commercial fertilizer were set 5 levels, intercross grouping, repeat 4 times. The results of different group are list in table 4.Table 4 The yield of the result of different groupB1B2B3B4B5A12726313025292530

37、302526243031262629313024A23028313228302731342928263033282925323227A33333353530333433342934343733313235353530Triple（3）Case 1 The experiment studied the relationship between the yield of cotton and other factors by randomized blocks design. Factor A is variety, A1 is upland cotton; A2 is Levant cotton

38、. Factor B is sowing time, B1 is sowing in Grain rain; B2 is sowing in Summer begins. Factor C is density, C1 is 3500 plants each 666.7m2; C2 is 7000 plants each 666.7m2; C3 is 10500. The area of yield is 40m2, repeats 3 times. The results of each treatment are list in the table 1.Table 1 The yield

39、of each treatmentTreatments BlocksA1B1C1121413C2121111C31099B2C11099C2998C3667A2B1C1324C2434C3767B2C1223C2345C3577Case 2 The experiment studied on the drought resistant and heat resistance of some buckwheat. Factor A is variety, A1 is America buckwheat; A2 is Tongxuan90 buckwheat; A3 is Meng87 buckw

40、heat; A4 is Daheisanleng buckwheat. Factor B is period of time of treatment, B1 is 18 hours; B2 is 24 hours; B3 is 48 hours. Factor C is temperature of heat treatment about one hours, C1 is 36; C2 is 38.After the treatment of drought and heat, we cut down root tip 23mm of the germinating seed, and t

41、hen staining it with iodine solution and calculating the hydrolysis of starch grain number. The hydrolyze rate of buckwheat of different treatments are list in table 2：Table 2 The hydrolyze rate of buckwheat of different treatmentsTreatmentsHydrolyze rate（%）A1B1C168C273B2C178C293B3C187C293A2B1C157C2

42、61B2C171C278B3C180C288A3B1C137C241B2C155C261B3C166C277A4B1C170C275B2C182C286B3C191C298Case 3 Soybean isoflavone and Soyasaponins are main secondary metabolite matter of soybean. The two all has many biological activity functions, such as curing and preventing cancer and cardiovascular disease and th

43、e like. In this experiment, 20 different type soybean varieties are selected as the research object. There are 9 seed-times to plant in two year stabs, and 360 soybeans samples are harvested altogether. The content of Soybean isoflavone and Soyasaponin is determined for all samples. Comparing the de

44、gree of the influence effect about variety、Sowing time and year factors for Soybean isoflavones and Soyasaponin content. Factor A is year, A1 is the year of 2004; A2 is the year of 2005. Factor B is varieties, B1 is Nanchun201; B2 is Wuchangliuyuebao; B3 is Junlianjiuzhuandou; B4 is TongdouNo.3; B5

45、is V97-5391; B6 is Shanzibai; B7 is Bamaliuyuehuang; B8 is Qidongyangyandou; B9 is JidouNo.10; B10 is Anjieqingdou; B11 is PI548662; B12 is J280082; B13 is 493-1; B14 is Chunpingxiaoziyaoheidou; B15 is SU-123; B16 is Zaotabianqing; B17 is Aolai; B18 is HeidouNo.1; B19 is Guiyangzijindou; B20 is Rudo

46、ngwanlvhuang; Factor C is sowing time, C1 is Mar.15; C2 is Apr.15; C3 is May 15; C4 is Jun 15; C5 is Jul.15; C6 is Aug.15.(In 2005,we just sowing soybean in C1、C2 and C3.) Then, we determined the content of Soybean isoflavone and Soyasaponin for 360 soybeans samples, the results are list in table 3.1 and 3.2.(1)、Try analyze the degree of the influence effect about variety and sowing time for Soybean isoflavone.(2)、Try analyze the degree of the influence effect about variety 、sowing time and year factors for Soybean isoflavone.Table 3.1 Soybean isoflavones accumulation qua