生物统计学答案 第八章 单因素方差分析.doc

第八章 单因素方差分析8.1 黄花蒿中所含的青蒿素是当前抗疟首选药物，研究不同播期对黄花蒿种子产量的影响，试验采用完全随机化设计，得到以下结果(kg/小区)47：重 复播 种 期2月19日3月9日3月28日4月13日10.260.140.120.0320.490.240.110.0230.360.210.150.04对上述结果做方差分析。答：所用程序及结果如下：options linesize=76 nodate;data mugwort;do date=1 to 4;do repetit=1 to 3;input yield ;output;end;end;cards;0.26 0.49 0.360.14 0.24 0.210.12 0.11 0.150.03 0.02 0.04;run;proc anova;class date;model yield=date;means date/duncan;run;One-Way ANOVAAnalysis of Variance ProcedureClass Level InformationClass Levels ValuesDATE 4 1 2 3 4Number of observations in data set = 12One-Way ANOVA Analysis of Variance ProcedureDependent Variable: YIELDSum of MeanSource DF Squares Square F Value Pr FModel 3 0.18515833 0.06171944 14.99 0.0012Error 8 0.03293333 0.00411667Corrected Total 11 0.21809167R-Square C.V. Root MSE YIELD Mean0.848993 35.48088 0.06416 0.18083Source DF Anova SS Mean Square F Value Pr FDATE 3 0.18515833 0.06171944 14.99 0.0012One-Way ANOVAAnalysis of Variance ProcedureDuncans Multiple Range Test for variable: YIELDNOTE: This test controls the type I comparisonwise error rate, notthe experimentwise error rateAlpha= 0.05 df= 8 MSE= 0.004117Number of Means 2 3 4Critical Range .1208 .1259 .1287Means with the same letter are not significantly different.Duncan Grouping Mean N DATEA 0.37000 3 1B 0.19667 3 2BC B 0.12667 3 3CC 0.03000 3 4对于方差分析表中各项内容的含义，在“SAS程序及释义”部分已经做了详细解释，这里不再重复。如果有不明白的地方，请复习“SAS程序及释义”的相关内容。SAS分析结果指出，不同播种期其产量差异极显著。多重比较表明，2和3间差异不显著，3和4间差异不显著，1和其他各组间差异都显著。以上结果可以归纳成下表。变差来源平方和自由度均方FP播期间0.185 158 3330.061 719 4414.990.001 2重复间0.032 933 3380.004 116 67总 和0.218 091 6711多重比较：12348.2 下表是6种溶液及对照组的雌激素活度鉴定，指标是小鼠子宫重。对表中的数据做方差分析，若差异是显著的，则需做多重比较。鼠 号溶 液 种 类(ck)189.984.464.475.288.456.465.6293.8116.079.862.490.283.279.4388.484.088.062.473.290.465.64112.668.669.473.887.885.670.2答：所用程序及结果如下：options linesize=76 nodate;data uterus;infile e:dataexr8-2e.dat;do solution=1 to 7;do repetit=1 to 4;input weight ;output;end;end;run;proc anova;class solution;model weight=solution;means solution/duncan;run;The SAS SystemAnalysis of Variance ProcedureClass Level InformationClass Levels ValuesSOLUTION 7 1 2 3 4 5 6 7Number of observations in data set = 28The SAS SystemAnalysis of Variance ProcedureDependent Variable: WEIGHTSum of MeanSource DF Squares Square F Value Pr FModel 6 2419.10500 403.18417 2.77 0.0385Error 21 3061.30750 145.77655Corrected Total 27 5480.41250R-Square C.V. Root MSE WEIGHT Mean0.441409 15.03118 12.0738 80.3250Source DF Anova SS Mean Square F Value Pr FSOLUTION 6 2419.10500 403.18417 2.77 0.0385The SAS SystemAnalysis of Variance ProcedureDuncans Multiple Range Test for variable: WEIGHTNOTE: This test controls the type I comparisonwise error rate, notthe experimentwise error rateAlpha= 0.05 df= 21 MSE= 145.7765Number of Means 2 3 4 5 6 7Critical Range 17.75 18.64 19.20 19.60 19.89 20.12Means with the same letter are not significantly different.Duncan Grouping Mean N SOLUTIONA 96.175 4 1AB A 88.250 4 2B AB A 84.900 4 5B AB A 78.900 4 6BB 75.400 4 3BB 70.200 4 7BB 68.450 4 4溶液种类的显著性概率P0.038 5，P FModel 3 353.750262 117.916754 3.92 0.0208Error 24 722.841310 30.118388Corrected Total 27 1076.591572R-Square C.V. Root MSE Y Mean0.328584 53.19776 5.48802 10.3163Source DF Anova SS Mean Square F Value Pr FCOLLOID 3 353.750262 117.916754 3.92 0.0208基质项的F值为3.92，F的显著性概率P0.020 8，故拒绝H0。在不同基质中已贴壁的组织块，其细胞分裂的百分数不同。以上结果可以归纳成下表：变差来源平方和自由度均方FP基质间353.750 2623117.916 7543.920.020 8重复间722.841 3102430.118 388总 和1 076.591 572278.4 不同年龄马鹿的下臼齿齿尖高度(mm)如下表所示48，用单因素方差分析推断，不同年龄组之间，下臼齿齿尖高度差异是否显著。重复年 龄 /a2.53.54.55.56.57.58.50116.7014.5313.8811.7210.309.0010.950218.9014.5015.8012.327.9011.008.900316.0514.8513.5011.658.558.8811.550415.4514.2011.4312.4711.129.1310.370514.8015.2212.3512.089.359.880614.7511.3512.3012.807.100714.9011.2811.128.787.600814.8514.3010.0810.150914.7014.108.901014.9013.6511.301114.4011.8510.581211.151311.601411.171511.151613.151713.78答：计算结果见下表：The SAS SystemAnalysis of Variance ProcedureClass Level InformationClass Levels ValuesAGES 7 1 2 3 4 5 6 7Number of observations in data set = 56The SAS SystemAnalysis of Variance ProcedureDependent Variable: HIGHTSum of MeanSource DF Squares Square F Value Pr FModel 6 253.766360 42.294393 23.37 0.0001Error 49 88.671661 1.809626Corrected Total 55 342.438021R-Square C.V. Root MSE HIGHT Mean0.741058 11.07929 1.34522 12.1418Source DF Anova SS Mean Square F Value Pr FAGES 6 253.766360 42.294393 23.37 0.0001年龄项的F23.37，其显著性概率P0.000 1。故拒绝H0。不同年龄马鹿的下臼齿齿尖高度差异极显著。以上结果可以归纳成下表：变差来源平方和自由度均方FP年龄间253.766 360642.294 39323.370.0001重复间88.671 661491.809 626总 和342.438 021558.5 由5个雄性和3个雌性黑线鳕的配子杂交，获得15个半同胞家系。研究同一个父亲不同母亲及同一个母亲不同父亲的后代在若干性状上的差异显著程度，推断双亲对后代各性状影响的大小。调查时间为幼鱼孵化出当天（0 dph）和孵化出第五天（5 dph）。下面仅列出其中5 dph幼鱼眼睛直径的单因素方差分析结果49。5 dph幼鱼眼睛直径（mm）的方差分析分 组变差来源 平方和自由度P雌鱼1雄鱼间5.110-440.015雄鱼内6.010-419总 和1.110-323雌鱼2雄鱼间1.610-420.053雄鱼内2.310-411总 和3.910-413雌鱼3雄鱼间1.710-540.842雄鱼内2.310-418总 和2.510-422雄鱼1雌鱼间1.010-310.001雌鱼内1.810-48总 和1.210-49雄鱼2雌鱼间7.910-420.001雌鱼内1.310-412总 和9.210-414雄鱼3雌鱼间1.110-320.001雌鱼内2.010-49总 和1.310-311雄鱼4雌鱼间1.710-32 FModel 3 7.33333333 2.44444444 1.33 0.2808Error 32 58.66666667 1.83333333Corrected Total 35 66.00000000R-Square C.V. Root MSE SCORE Mean0.111111 33.85016 1.35401 4.00000Source DF Anova SS Mean Square F Value Pr FCATEGORY 3 7.33333333 2.44444444 1.33 0.2808F的显著性概率P0.28，P 0.05，尚无足够的理由拒绝H0。四种果酒的得分差异不显著。以上结果可以归纳成下表：变差来源平方和自由度均方FP类别间7.3332.441.