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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：optionslinesize=76nodate;datamugwort;dodate=1to4;dorepetit=1to3;inputyield@@;output;end;end;cards;0.260.490.360.140.240.210.120.110.150.030.020.04;run;procanova;classdate;modelyield=date;meansdate/duncan;run;One-WayANOVAAnalysisofVarianceProcedureClassLevelInformationClassLevelsValuesDATE41234Numberofobservationsindataset=12One-WayANOVAAnalysisofVarianceProcedureDependentVariable:YIELDSumofMeanSourceDFSquaresSquareFValuePrFModel30.185158330.0617194414.990.0012Error80.032933330.00411667CorrectedTotal110.21809167R-SquareC.V.RootMSEYIELDMean0.84899335.480880.064160.18083SourceDFAnovaSSMeanSquareFValuePrFDATE30.185158330.0617194414.990.0012One-WayANOVAAnalysisofVarianceProcedureDuncan'sMultipleRangeTestforvariable:YIELDNOTE:ThistestcontrolsthetypeIcomparisonwiseerrorrate,nottheexperimentwiseerrorrateAlpha=0.05df=8MSE=0.004117NumberofMeans234CriticalRange.1208.1259.1287Meanswiththesameletterarenotsignificantlydifferent.DuncanGroupingMeanNDATEA0.3700031B0.1966732BCB0.1266733CC0.0300034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0.1851583330.0617194414.990.0012重复间0.0329333380.00411667总和0.2180916711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Ⅰ(ck)ⅡⅢⅣⅤⅥⅦ189.984.464.475.288.456.465.6293.8116.079.862.490.283.279.4388.484.088.062.473.290.465.64112.668.669.473.887.885.670.2答：所用程序及结果如下：optionslinesize=76nodate;datauterus;infile'e:\data\exr8-2e.dat';dosolution=1to7;dorepetit=1to4;inputweight@@;output;end;end;run;procanova;classsolution;modelweight=solution;meanssolution/duncan;run;TheSASSystemAnalysisofVarianceProcedureClassLevelInformationClassLevelsValuesSOLUTION71234567Numberofobservationsindataset=28TheSASSystemAnalysisofVarianceProcedureDependentVariable:WEIGHTSumofMeanSourceDFSquaresSquareFValuePrFModel62419.10500403.184172.770.0385Error213061.30750145.77655CorrectedTotal275480.41250R-SquareC.V.RootMSEWEIGHTMean0.44140915.0311812.073880.3250SourceDFAnovaSSMeanSquareFValuePrFSOLUTION62419.10500403.184172.770.0385TheSASSystemAnalysisofVarianceProcedureDuncan'sMultipleRangeTestforvariable:WEIGHTNOTE:ThistestcontrolsthetypeIcomparisonwiseerrorrate,nottheexperimentwiseerrorrateAlpha=0.05df=21MSE=145.7765NumberofMeans234567CriticalRange17.7518.6419.2019.6019.8920.12Meanswiththesameletterarenotsignificantlydifferent.DuncanGroupingMeanNSOLUTIONA96.17541ABA88.25042BABA84.90045BABA78.90046BB75.40043BB70.20047BB68.45044溶液种类的显著性概率P＝0.0385，P0.05，不同种类的溶液影响显著。其中1、2、5、6间差异不显著；2、5、6、3、7、4间差异不显著。以上结果可以归纳成下表：变差来源平方和自由度均方FP溶液间2419.105006403.184172.770.0385重复间3061.3075021145.77655总和5480.41250271(ck)2563748.3人类绒毛组织培养，通常的方法是，向培养瓶中接入大量组织碎片，加入适当的基质使组织碎片贴壁，经过一段时间，将贴壁的组织块浸入到培养基中。下表给出了贴壁的组织块，其细胞已开始分裂的百分数：例数基质种类鸡血浆人血浆鼠尾胶原不加基质14.62.62.60214.612.511.24.5311.18.71.21.144.72.21.80.0458.80.090.02062.64.83.43.373.25.44.01.1对以上数据做方差分析。（提示：这里的数据是百分数，见§9.7）答：因为数据是百分数，为了满足方差齐性的要求，需做反正弦变换。这时需要在DATA步中加入赋值语句，(变量)=arsin(sqrt(y/100))*180/3.14159265。程序和计算结果如下：optionslinesize=76nodate;datachorion;infile'e:\data\exr8-3e.dat';docolloid=1to4;dorepetit=1to7;inputpercen@@;y=arsin(sqrt(percen/100))*180/3.14159265;output;end;end;run;procanova;classcolloid;modely=colloid;meanscolloid/duncan;run;TheSASSystemAnalysisofVarianceProcedureClassLevelInformationClassLevelsValuesCOLLOID41234Numberofobservationsindataset=28TheSASSystemAnalysisofVarianceProcedureDependentVariable:YSumofMeanSourceDFSquaresSquareFValuePrFModel3353.750262117.9167543.920.0208Error24722.84131030.118388CorrectedTotal271076.591572R-SquareC.V.RootMSEYMean0.32858453.197765.4880210.3163SourceDFAnovaSSMeanSquareFValuePrFCOLLOID3353.750262117.9167543.920.0208基质项的F值为3.92，F的显著性概率P＝0.0208，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353.7502623117.9167543.920.0208重复间722.8413102430.118388总和1076.591572278.4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：TheSASSystemAnalysisofVarianceProcedureClassLevelInformationClassLevelsValuesAGES71234567Numberofobservationsindataset=56TheSASSystemAnalysisofVarianceProcedureDependentVariable:HIGHTSumofMeanSourceDFSquaresSquareFValuePrFModel6253.76636042.29439323.370.0001Error4988.6716611.809626CorrectedTotal55342.438021R-SquareC.V.RootMSEHIGHTMean0.74105811.079291.3452212.1418SourceDFAnovaSSMeanSquareFValuePrFAGES6253.76636042.29439323.370.0001年龄项的F＝23.37，其显著性概率P＝0.0001。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253.766360642.29439323