生物統(tǒng)計學(xué)(第3版)杜榮騫 課后習(xí)題答案 第八章 單因素方差分析.doc

第八章 單因素方差分析8.1 黃花蒿中所含的青蒿素是當(dāng)前抗瘧首選藥物，研究不同播期對黃花蒿種子產(chǎn)量的影響，試驗采用完全隨機化設(shè)計，得到以下結(jié)果(kg/小區(qū))47：重 復(fù)播 種 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對上述結(jié)果做方差分析。答：所用程序及結(jié)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 ANOVA Analysis of Variance Procedure Class Level Information Class Levels Values DATE 4 1 2 3 4 Number of observations in data set = 12 One-Way ANOVA Analysis of Variance ProcedureDependent Variable: YIELD Sum 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 0.21809167 R-Square C.V. Root MSE YIELD Mean 0.848993 35.48088 0.06416 0.18083Source DF Anova SS Mean Square F Value Pr FDATE 3 0.18515833 0.06171944 14.99 0.0012 One-Way ANOVA Analysis of Variance Procedure Duncans Multiple Range Test for variable: YIELD NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate Alpha= 0.05 df= 8 MSE= 0.004117 Number of Means 2 3 4 Critical Range .1208 .1259 .1287 Means with the same letter are not significantly different. Duncan Grouping Mean N DATE A 0.37000 3 1 B 0.19667 3 2 B C B 0.12667 3 3 C C 0.03000 3 4對于方差分析表中各項內(nèi)容的含義，在“SAS程序及釋義”部分已經(jīng)做了詳細解釋，這里不再重復(fù)。如果有不明白的地方，請復(fù)習(xí)“SAS程序及釋義”的相關(guān)內(nèi)容。SAS分析結(jié)果指出，不同播種期其產(chǎn)量差異極顯著。多重比較表明，2和3間差異不顯著，3和4間差異不顯著，1和其他各組間差異都顯著。以上結(jié)果可以歸納成下表。變差來源平方和自由度均方FP播期間0.185 158 3330.061 719 4414.990.001 2重復(fù)間0.032 933 3380.004 116 67總 和0.218 091 6711 多重比較：12348.2 下表是6種溶液及對照組的雌激素活度鑒定，指標是小鼠子宮重。對表中的數(shù)據(jù)做方差分析，若差異是顯著的，則需做多重比較。鼠 號溶 液 種 類(ck)1 89.984.464.475.288.456.465.62 93.8116.079.862.490.283.279.43 88.484.088.062.473.290.465.64112.668.669.473.887.885.670.2答：所用程序及結(jié)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 System Analysis of Variance Procedure Class Level Information Class Levels Values SOLUTION 7 1 2 3 4 5 6 7 Number of observations in data set = 28 The SAS System Analysis of Variance ProcedureDependent Variable: WEIGHT Sum 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 5480.41250 R-Square C.V. Root MSE WEIGHT Mean 0.441409 15.03118 12.0738 80.3250Source DF Anova SS Mean Square F Value Pr FSOLUTION 6 2419.10500 403.18417 2.77 0.0385 The SAS System Analysis of Variance Procedure Duncans Multiple Range Test for variable: WEIGHT NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate Alpha= 0.05 df= 21 MSE= 145.7765 Number of Means 2 3 4 5 6 7 Critical Range 17.75 18.64 19.20 19.60 19.89 20.12 Means with the same letter are not significantly different. Duncan Grouping Mean N SOLUTION A 96.175 4 1 A B A 88.250 4 2 B A B A 84.900 4 5 B A B A 78.900 4 6 B B 75.400 4 3 B B 70.200 4 7 B B 68.450 4 4溶液種類的顯著性概率P0.038 5，P FModel 3 353.750262 117.916754 3.92 0.0208Error 24 722.841310 30.118388Corrected Total 27 1076.591572 R-Square C.V. Root MSE Y Mean 0.328584 53.19776 5.48802 10.3163Source DF Anova SS Mean Square F Value Pr FCOLLOID 3 353.750262 117.916754 3.92 0.0208基質(zhì)項的F值為3.92，F(xiàn)的顯著性概率P0.020 8，故拒絕H0。在不同基質(zhì)中已貼壁的組織塊，其細胞分裂的百分數(shù)不同。以上結(jié)果可以歸納成下表：變差來源平方和自由度均方FP基質(zhì)間353.750 2623117.916 7543.920.020 8重復(fù)間722.841 3102430.118 388總 和1 076.591 572278.4 不同年齡馬鹿的下臼齒齒尖高度(mm)如下表所示48，用單因素方差分析推斷，不同年齡組之間，下臼齒齒尖高度差異是否顯著。重復(fù)年 齡 /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：計算結(jié)果見下表： The SAS System Analysis of Variance Procedure Class Level Information Class Levels Values AGES 7 1 2 3 4 5 6 7 Number of observations in data set = 56 The SAS System Analysis of Variance ProcedureDependent Variable: HIGHT Sum of MeanSource DF Squares Square F Value Pr FModel 6 253.766360 42.294393 23.37 0.0001Error 49 88.671661 1.809626Corrected Total 55 342.438021 R-Square C.V. Root MSE HIGHT Mean 0.741058 11.07929 1.34522 12.1418Source DF Anova SS Mean Square F Value Pr FAGES 6 253.766360 42.294393 23.37 0.0001年齡項的F23.37，其顯著性概率P0.000 1。故拒絕H0。不同年齡馬鹿的下臼齒齒尖高度差異極顯著。以上結(jié)果可以歸納成下表：變差來源平方和自由度均方FP年齡間253.766 360642.294 39323.370.0001重復(fù)間88.671 661491.809 626總 和342.438 021558.5 由5個雄性和3個雌性黑線鱈的配子雜交，獲得15個半同胞家系。研究同一個父親不同母親及同一個母親不同父親的后代在若干性狀上的差異顯著程度，推斷雙親對后代各性狀影響的大小。調(diào)查時間為幼魚孵化出當(dāng)天（0 dph）和孵化出第五天（5 dph）。下面僅列出其中5 dph幼魚眼睛直徑的單因素方差分析結(jié)果49。5 dph幼魚眼睛直徑（mm）的方差分析分 組變差來源 平方和自由度P雌魚1雄魚間5.110-440.015雄魚內(nèi)6.010-419總 和1.110-323雌魚2雄魚間1.610-420.053雄魚內(nèi)2.310-411總 和3.910-413雌魚3雄魚間1.710-540.842雄魚內(nèi)2.310-418總 和2.510-422雄魚1雌魚間1.010-310.001雌魚內(nèi)1.810-48總 和1.210-49雄魚2雌魚間7.910-420.001雌魚內(nèi)1.310-412總 和9.210-414雄魚3雌魚間1.110-320.001雌魚內(nèi)2.010-49總 和1.310-311雄魚4雌魚間1.710-32 FModel 3 7.33333333 2.44444444 1.33 0.2808Error 32 58.66666667 1.83333333Corrected Total 35 66.00000000 R-Square C.V. Root MSE SCORE Mean 0.111111 33.85016 1.35401 4.00000Source DF Anova SS Mean Square F Value Pr FCATEGORY 3 7.33333333 2.44444444 1.33 0.2808F的顯著性概率P0.28，P 0.05，尚無足夠的理由拒絕H0。四種果酒的得分差異不顯著。以上結(jié)果可以歸納成下表：變差來源平方和自由度均方FP類別間7.3332.