单因素方差分析示例1

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。

 

     

(ck)

1

 89.9

84.4

64.4

75.2

88.4

56.4

65.6

2

 93.8

116.0

79.8

62.4

90.2

83.2

79.4

3

 88.4

84.0

88.0

62.4

73.2

90.4

65.6

4

112.6

68.6

69.4

73.8

87.8

85.6

70.2

答:所用程序及结果如下:

options linesize=76 nodate;

data uterus;

    infile 'e:\data\exr8-2e.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 Procedure

 

Dependent Variable: WEIGHT

                                   Sum of          Mean

Source                  DF        Squares        Square   F Value     Pr > F

 

Model                    6     2419.10500     403.18417      2.77     0.0385

 

Error                   21     3061.30750     145.77655

 

Corrected Total         27     5480.41250

 

                  R-Square           C.V.      Root MSE          WEIGHT Mean

 

                  0.441409       15.03118       12.0738              80.3250

 

 

Source                  DF       Anova SS   Mean Square   F Value     Pr > F

 

SOLUTION                 6     2419.10500     403.18417      2.77     0.0385

 

                               The SAS System

 

                       Analysis of Variance Procedure

 

             Duncan's 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

溶液种类的显著性概率P0.038 5P <0.05,不同种类的溶液影响显著。其中1256间差异不显著;256374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

F

P

溶液间

2 419.105 00

6

403.184 17

2.77

0.038 5

重复间

3 061.307 50

21

145.776 55

 

 

 

5 480.412 50

27

 

 

 

 

1(ck)

2

5

6

3

7

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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