ANOVA分析例题

.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：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，得资料如下表2，试检验品种穗长间有无差异。（各处理的重复数不等）表2 5个玉米品种的穗长品种穗长（cm）重复数B121.519.5202218206B21618.51715.520166B31917.52018175B42118.519204B515.51817164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体重（斤），试分析母猪对仔猪体重效应的差异显著性。（每组样本容量不等）表3 三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）品种区组（重复）农海6753525051十石52585557农林8758565353农林1853515455 例5、将一种生长激素配成M1、M2、M3、M4、M5五种浓度，并用H1、H2、H3、三种时间浸渍某大豆品种的种子，45天后得各处理每一植株的平均干物重（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Mi（生长激素）Hi（时间）H1H2H3M1131414M2121213M3333M410910M5254小区内有重复观察值 例6、北京农业大学以45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，其中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 组合12345123451234511516171516151515161515141516162151516151515151415161514151616314141513141616141615161415151641516161516151615161515171714155161717171716171817171819171718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7 5个杂优水稻品种干物质积累资料重复 品种1234512345A7.88.99.211.410.512.110.68.79.910.1B7.48.88.97.89.86.26.65.37.58.1C12.610.211.411.812.115.215.112.312.512.9D5.84.76.67.47.96.46.88.17.27.9E13.815.113.412.616.611.717.215.615.115.8Double（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6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地块（A）田间管理方法（B）B1(化学控制)B2（集成虫害管理）B3（改良集成虫害管理）A1717377A2909092A3597080A4758082A5656067A6828685例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A1B1616261B2606162B3616161A2B1606061B2605961B3626061A3B1606062B2636463B3606061两因素随机区组试验的方差分析例3、将水稻的3个不同细胞质源的不育系（A1、A2、A3）和5个恢复系（B1、B2、B3、B4、B5）杂交，配成15个F1。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、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）B1B2B3B4B5A12726313025292530302526243031262629313024A23028313228302731342928263033282925323227A33333353530333433342934343733313235353530Triple（3）三因素随机区组试验的方差分析例1、有一棉花栽培试验，A因素为品种，有A1=陆地棉，A2=草棉两个水平；B因素为播期，B1=谷雨播，B2=立夏播两个水平；C因素为密度，C1=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A1B1C1121413C2121111C31099B2C11099C2998C3667A2B1C1324C2434C3767B2C1223C2345C3577例2、有一荞麦品种抗旱性和耐热性试验，A因素为品种，A1=美国荞麦，A2=通选90荞麦，A3=蒙87荞麦，A4=大黑三棱荞麦；B因素为时间（种子处理：取饱满发芽力强的四种荞麦种子分别放于室温中浸润吸水，然后放于温箱中25下发芽，芽长1cm时取出分别进行干处理的时间），B1=18小时，B2=24小时，B3=48小时；C因素为温度（干处理完在分别进行热处理1小时），C1=36，C2=38。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，放于显微镜下观察各个不同温度、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 荞麦品种淀粉水解率表处 理水解率（%）A1B1C168C273B2C178C293B3C187C293A2B1C157C261B2C171C278B3C180C288A3B1C137C241B2C155C261B3C166C277A4B1C170C275B2C182C286B3C191C298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，A1=2004年，A2=2005年；B因素为品种，B1=南春201，B2=武昌六月爆，B3=筠连九转豆，B4=通豆3号，B5=V97-5391，B6=扇子白，B7=巴马九月黄，B8=启东羊眼豆，B9=冀豆10号，B10=安吉青豆，B11=PI548662，B12=J280082，B13=493-1，B14=淳平小子药黑豆，B15=SU-123，B16=早踏扁青，B17=奥莱，B18=黑豆一号，B19=桂阳紫金豆，B20=如东晚绿黄； C因素为播期，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，而同一品种在播期不同的情况下也有差异，对品种和播期作二因素分析。）（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（C2）、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）各品种所对应的异黄酮含量值组成三因素方差分析表。）表3.1 2004年各播期大豆籽粒总异黄酮积累量（g/g）Table3.1 Soybean isoflavones accumulation quantity of every sowing time in 2004B:品种名称(variety)C:播 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 筠连九转豆668.58 741.24 1117.19 2405.41 2963.95 2840.79 通豆3号1939.45 2104.13 2365.35 2518.47 3099.27 2944.75 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 巴马九月黄1772.88 2029.19 2124.11 2333.26 2433.31 2637.33 启东羊眼豆1310.44 1281.47 1316.35 1543.75 1817.63 2275.84 冀豆10号749.22 617.75 933.48 2190.79 3378.07 4564.56 安吉青豆1700.00 1920.70 2137.61 1940.68 2760.10 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 淳平小子药黑豆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 1160.83 1400.95 1762.44 2652.06 2454.63 奥莱355.69 403.68 574.00 1489.56 1327.09 2515.46 黑豆一号1378.13 630.58 372.38 1095.31 1870.09 3580.86 桂阳紫金豆1204.85 962.50 1660.83 2380.36 2974.11 3826.84 如东晚绿黄2481.53 2597.77 2576.62 3339.51 3639.29 2653.07 表3.2 2005年各播期大豆籽粒总异黄酮积累量（g/g）Table3.1 Soybean isoflavones accumulation quantity of every sowing time in 2005B:品种名称(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 筠连九转豆652.29 1494.48 2980.69 通豆3号1200.89 2423.44 3510.49 V97-5391751.28 2556.03 3048.49 扇子白1749.16 2284.04 2875.06 巴马九月黄1329.07 2024.33 2862.83 启东羊眼豆826.06 1257.03 2379.41 冀豆10号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 淳平小子药黑豆833.43 1147.66 2687.22 SU-123659.32 1354.13 2823.10 早踏扁青663.56 1450.84 2791.74 奥莱255.97 1158.54 1931.03 黑豆一号832.42 680.19 3158.37 桂阳紫金豆1463.84 2380.36 3590.57 如东晚绿黄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. 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 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）RepeatsB121.519.5202218206B21618.51715.520166B31917.52018175B42118.519204B515.51817164Case 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.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 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. 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 45 crosses experiment by randomized blocks design method. There are 3 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 materialRepeatsCrosses12345123451234511516171516151515161515141516162151516151515151415161514151616314141513141616141615161415151641516161516151615161515171714155161717171716171817171819171718Nongda 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 given 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 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 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 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 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 are 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, 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 groupB1B2B3B4B5A12726313025292530302526243031262629313024A23028313228302731342928263033282925323227A33333353530333433342934343733313235353530Triple（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. 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 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 buckwheat; 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 then 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（%）A1B1C168C273B2C178C293B3C187C293A2B1C157C261B2C171C278B3C180C288A3B1C137C241B2C155C261B3C166C277A4B1C170C275B2C182C286B3C191C298Case 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 the 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 degree 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 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 Rudongwanlvhuang; 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