神马文学网SAS常用程序(4)
来源：百度文库 编辑：神马文学网 时间：2024/05/04 08:05:13
2.5 常用实验设计方差分析的SAS程序
在这本教材中我们只介绍了完全随机化实验设计和交叉分组实验设计的方差分析。除这两种实验设计外，还有很多实验设计需要用方差分析的方法处理数据。如随机化完全区组设计、拉丁方设计、裂区设计、套设计、正交设计等。这些实验设计方法在很多教材中都可以找到，限于篇幅在这里就不做更多的介绍了，只给出线性统计模型、均方期望和检验统计量。完全随机化实验设计的SAS程序在§ 2.4中已经做过介绍，这一节将给出其它一些实验设计方差分析的SAS程序。在阅读以下内容之前，请先阅读第一章“SAS软件基本操作”。
三因素交叉分组实验的方差分析
在课本9.5.3中已经给出了一个混合模型（A、C固定，B随机）三因素交叉分组实验设计的均方期望及检验统计量。下面以一个一般化的三因素交叉分组实验为例说明方差分析的SAS程序。
例 2.10 由A、B、C三个因素构成一个三因素交叉分组实验，其中A、C固定，B随机。A因素有三个水平，记为A1－A3；B因素有四个水平，记为B1－B4；C因素有五个水平，记为C1－C5，实验重复两次。记录了R1和R2两个因变量（即实验结果，如作物的株高、穗长，人的血压、血黏度等），原始数据不再给出。按每一观测的A、B、C、R1、R2的顺序建立外部数据文件，路径和文件名为a:\2-6data.dat。
1 1 1 18.0 24.1 1 1 2 19.6 24.7 1 1 3 17.5 24.7 1 1 4 17.9 25.8
1 1 5 19.1 25.2 1 2 1 23.4 33.4 1 2 2 23.0 33.2 1 2 3 23.9 32.9
1 2 4 23.2 34.3 1 2 5 27.0 35.0 1 3 1 24.5 29.6 1 3 2 23.7 30.8
1 3 3 23.5 31.7 1 3 4 21.2 32.2 1 3 5 25.7 31.9 1 4 1 19.4 27.6
1 4 2 17.3 27.8 1 4 3 18.1 28.0 1 4 4 18.8 28.7 1 4 5 18.8 28.4
2 1 1 18.8 28.7 2 1 2 19.6 28.6 2 1 3 18.6 29.8 2 1 4 18.2 30.1
2 1 5 20.8 31.0 2 2 1 24.2 38.2 2 2 2 24.4 37.9 2 2 3 25.3 38.3
2 2 4 24.0 38.6 2 2 5 27.3 33.7 2 3 1 25.9 35.1 2 3 2 23.6 34.4
2 3 3 23.8 36.1 2 3 4 21.1 35.9 2 3 5 26.4 36.4 2 4 1 18.9 34.2
2 4 2 21.9 31.9 2 4 3 23.5 32.3 2 4 4 20.0 33.0 2 4 5 20.4 33.3
3 1 1 19.2 31.2 3 1 2 19.6 30.6 3 1 3 19.2 32.5 3 1 4 18.9 33.1
3 1 5 20.0 32.3 3 2 1 22.6 38.7 3 2 2 23.4 39.4 3 2 3 25.5 41.0
3 2 4 24.2 41.2 3 2 5 28.3 42.4 3 3 1 25.3 36.3 3 3 2 23.9 37.2
3 3 3 23.8 36.9 3 3 4 21.2 38.4 3 3 5 25.4 37.4 3 4 1 17.2 30.9
3 4 2 17.9 32.0 3 4 3 20.8 31.8 3 4 4 18.2 33.1 3 4 5 16.4 31.5
1 1 1 18.3 24.4 1 1 2 19.2 24.2 1 1 3 18.4 25.5 1 1 4 18.1 26.3
1 1 5 19.2 25.3 1 2 1 23.3 33.2 1 2 2 23.0 32.9 1 2 3 25.1 34.2
1 2 4 24.6 35.6 1 2 5 26.0 34.0 1 3 1 24.5 29.5 1 3 2 23.1 30.0
1 3 3 23.0 31.1 1 3 4 20.3 31.3 1 3 5 25.5 31.4 1 4 1 19.6 27.4
1 4 2 19.8 25.9 1 4 3 22.2 27.3 1 4 4 19.5 28.5 1 4 5 19.6 28.1
2 1 1 18.0 28.0 2 1 2 19.6 28.4 2 1 3 19.3 30.6 2 1 4 18.0 30.0
2 1 5 20.1 30.3 2 2 1 24.0 38.8 2 2 2 23.8 37.4 2 2 3 24.2 36.9
2 2 4 24.2 38.9 2 2 5 27.8 37.0 2 3 1 25.6 34.7 2 3 2 23.4 34.0
2 3 3 23.7 35.7 2 3 4 20.6 35.3 2 3 5 26.1 35.9 2 4 1 20.4 32.3
2 4 2 24.6 34.6 2 4 3 23.9 32.8 2 4 4 21.1 34.1 2 4 5 20.0 33.0
3 1 1 18.3 30.1 3 1 2 19.8 31.0 3 1 3 17.6 30.6 3 1 4 17.9 31.9
3 1 5 20.8 32.8 3 2 1 23.4 39.8 3 2 2 23.4 39.4 3 2 3 26.5 41.7
3 2 4 24.4 41.6 3 2 5 27.1 41.3 3 3 1 25.6 36.6 3 3 2 23.5 37.0
3 3 3 23.7 37.9 3 3 4 21.4 38.4 3 3 5 25.5 37.5 3 4 1 17.5 31.5
3 4 2 19.5 31.6 3 4 3 21.7 32.4 3 4 4 18.4 33.4 3 4 5 16.5 31.5
解：SAS程序如下：
options linesize=76;
data example;
infile ‘a:\2-6data.dat’;
input a b c r1 r2 @@;
run;
proc anova;
class a b c;
model r1 r2 = a b c a*b a*c b*c a*b*c;
test h = a e = a*b;
test h = c e = b*c;
test h = a*c e = a*b*c;
means a / duncan e = a*b alpha = 0.01;
means c / lsd e = b*c alpha = 0.01;
run;
与单因素方差分析的SAS程序相比，大同小异。在这里由于因素由1个变为3个，因此分类变量相应变为3个。在MODEL语句中r1 r2 = a b c a*b a*c b*c a*b*c; 的含义是，需要分析a、b、c三个主效应，两两交互作用及三重交互作用对因变量r1和r2的贡献。实际上，这里是两次方差分析，得到两个方差分析表，一个是对r1进行的方差分析，一个是对r2进行的方差分析。当然也可以只计算其中的一部分，如r1 r2 = a b c b*c或r2 = a b c a*b a*b*c 等。
TEST语句中h = a e = a*b 的含义是用A´B交互作用检验A因素效应，即FA ＝MSA / MSAB，另外两个TEST语句含义为FC＝MSC / MSBC，FAC＝MSAC / MSABC。在没有特别说明时，因素的效应都是用MSe检验的（见课本9.5.3）。当然，随着模型的改变，检验统计量会相应改变，这里的TEST语句也要改变。
MEANS语句中选项e = a*b是指明在做DUNCAN检验时，应使用MSAB作为误差均方检验因素A的效应，否则将使用MSe做检验。
实验结果中，若有缺失数据，缺失的数据在方差分析中将被忽略掉，因此实验结果中的数据应完整。
执行上述程序，输出的结果见表2－14。
表2－14 例2.10方差分析输出的结果
The SAS System
Analysis of Variance Procedure
Class Level Information
Class
Levels
Values
A
3
1 2 3
B
4
1 2 3 4
C
5
1 2 3 4 5
Number of observations in data set = 120
The SAS System
Analysis of Variance Procedure
Dependent Variable: R1
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
59
1028.71625
17.43587
35.88
0.0001
Error
60
29.15500
0.48592
Correted Total
119
1057.87125
R-Square
C.V.
Root MSE
R1 Mean
0.972440
3.199437
0.69708
21.7875
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
21.608000
10.804000
22.23
0.0001
B
3
748.776917
249.592306
513.65
0.0001
C
4
68.006667
17.001667
34.99
0.0001
A*B
6
34.511333
5.751889
11.84
0.0001
A*C
8
6.035333
0.754417
1.55
0.1586
B*C
12
129.352667
10.779389
22.18
0.0001
A*B*C
24
20.425333
0.851056
1.75
0.0412
Tests of Hypotheses using the Anova MS for A*B as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
21.6080000
10.8040000
1.88
0.2326
Tests of Hypotheses using the Anova MS for B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
C
4
68.0066667
17.0016667
1.58
0.2432
Tests of Hypotheses using the Anova MS for A*B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A*C
8
6.03533333
0.75441667
0.89
0.5421
The SAS System
Analysis of Variance Procedure
Dependent Variable: R2
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
59
2224.52967
37.70389
85.85
0.0001
Error
60
26.35000
0.43917
Corrected Total
119
2250.87967
R-Square
C.V.
Root MSE
R2 Mean
0.988293
2.014173
0.66270
32.9017
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
779.20117
389.60058
887.14
0.0001
B
3
1314.66700
438.22233
997.85
0.0001
C
4
38.03300
9.50825
21.65
0.0001
A*B
6
53.47350
8.91225
20.29
0.0001
A*C
8
5.84050
0.73006
1.66
0.1266
B*C
12
7.51300
0.62608
1.43
0.1798
A*B*C
24
25.80150
1.07506
2.45
0.0027
Tests of Hypotheses using the Anova MS for A*B as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
779.201167
389.600583
43.72
0.0003
Tests of Hypotheses using the Anova MS for B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
C
4
38.0330000
9.5082500
15.19
0.0001
Tests of Hypotheses using the Anova MS for A*B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A*C
8
5.84050000
0.73006250
0.68
0.7052
The SAS System
Analysis of Variance Procedure
Duncan's Multiple Range Test for variable: R1
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha=0.01 df=6 MSE=5.751889
Number of Means
2
3
Critical Range
1.988
2.063
Means with the same letter are not significantly different.
Duncan Grouping
Mean
N
A
A
22.3775
40
2
A
A
21.5875
40
3
A
A
21.3975
40
1
The SAS System
Analysis of Variance Procedure
Duncan's Multiple Range Test for variable: R2
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha=0.01 df=6 MSE=8.91225
Number of Means
2
3
Critical Range
2.475
2.567
Means with the same letter are not significantly different.
Duncan Grouping
Mean
N
A
A
35.3975
40
3
A
A
33.9050
40
2
B
29.4025
40
1
The SAS System
Analysis of Variance Procedure
T tests (LSD) for variable: R1
NOTE: This test controls the type I comparisonwise error rate not
the experimentwise error rate.
Alpha=0.01 df=12 MSE=10.77939
Critical Value of T=3.05
Least Significant Difference=2.895
Means with the same letter are not significantly different.
T Grouping
Mean
N
C
A
22.9083
24
5
A
A
22.2000
24
3
A
A
21.6917
24
2
A
A
21.4958
24
1
A
A
20.6417
24
4
The SAS System
Analysis of Variance Procedure
T tests (LSD) for variable: R2
NOTE: This test controls the type I comparisonwise error rate not
the experimentwise error rate.
Alpha=0.01 df=12 MSE=0.626083
Critical Value of T=3.05
Least Significant Difference= 0.6977
Means with the same letter are not significantly different.
T Grouping
Mean
N
C
A
33.7375
24
4
A
B A
33.1917
24
5
B
B
33.0292
24
3
C
32.2875
24
2
C
在这本教材中我们只介绍了完全随机化实验设计和交叉分组实验设计的方差分析。除这两种实验设计外，还有很多实验设计需要用方差分析的方法处理数据。如随机化完全区组设计、拉丁方设计、裂区设计、套设计、正交设计等。这些实验设计方法在很多教材中都可以找到，限于篇幅在这里就不做更多的介绍了，只给出线性统计模型、均方期望和检验统计量。完全随机化实验设计的SAS程序在§ 2.4中已经做过介绍，这一节将给出其它一些实验设计方差分析的SAS程序。在阅读以下内容之前，请先阅读第一章“SAS软件基本操作”。
三因素交叉分组实验的方差分析
在课本9.5.3中已经给出了一个混合模型（A、C固定，B随机）三因素交叉分组实验设计的均方期望及检验统计量。下面以一个一般化的三因素交叉分组实验为例说明方差分析的SAS程序。
例 2.10 由A、B、C三个因素构成一个三因素交叉分组实验，其中A、C固定，B随机。A因素有三个水平，记为A1－A3；B因素有四个水平，记为B1－B4；C因素有五个水平，记为C1－C5，实验重复两次。记录了R1和R2两个因变量（即实验结果，如作物的株高、穗长，人的血压、血黏度等），原始数据不再给出。按每一观测的A、B、C、R1、R2的顺序建立外部数据文件，路径和文件名为a:\2-6data.dat。
1 1 1 18.0 24.1 1 1 2 19.6 24.7 1 1 3 17.5 24.7 1 1 4 17.9 25.8
1 1 5 19.1 25.2 1 2 1 23.4 33.4 1 2 2 23.0 33.2 1 2 3 23.9 32.9
1 2 4 23.2 34.3 1 2 5 27.0 35.0 1 3 1 24.5 29.6 1 3 2 23.7 30.8
1 3 3 23.5 31.7 1 3 4 21.2 32.2 1 3 5 25.7 31.9 1 4 1 19.4 27.6
1 4 2 17.3 27.8 1 4 3 18.1 28.0 1 4 4 18.8 28.7 1 4 5 18.8 28.4
2 1 1 18.8 28.7 2 1 2 19.6 28.6 2 1 3 18.6 29.8 2 1 4 18.2 30.1
2 1 5 20.8 31.0 2 2 1 24.2 38.2 2 2 2 24.4 37.9 2 2 3 25.3 38.3
2 2 4 24.0 38.6 2 2 5 27.3 33.7 2 3 1 25.9 35.1 2 3 2 23.6 34.4
2 3 3 23.8 36.1 2 3 4 21.1 35.9 2 3 5 26.4 36.4 2 4 1 18.9 34.2
2 4 2 21.9 31.9 2 4 3 23.5 32.3 2 4 4 20.0 33.0 2 4 5 20.4 33.3
3 1 1 19.2 31.2 3 1 2 19.6 30.6 3 1 3 19.2 32.5 3 1 4 18.9 33.1
3 1 5 20.0 32.3 3 2 1 22.6 38.7 3 2 2 23.4 39.4 3 2 3 25.5 41.0
3 2 4 24.2 41.2 3 2 5 28.3 42.4 3 3 1 25.3 36.3 3 3 2 23.9 37.2
3 3 3 23.8 36.9 3 3 4 21.2 38.4 3 3 5 25.4 37.4 3 4 1 17.2 30.9
3 4 2 17.9 32.0 3 4 3 20.8 31.8 3 4 4 18.2 33.1 3 4 5 16.4 31.5
1 1 1 18.3 24.4 1 1 2 19.2 24.2 1 1 3 18.4 25.5 1 1 4 18.1 26.3
1 1 5 19.2 25.3 1 2 1 23.3 33.2 1 2 2 23.0 32.9 1 2 3 25.1 34.2
1 2 4 24.6 35.6 1 2 5 26.0 34.0 1 3 1 24.5 29.5 1 3 2 23.1 30.0
1 3 3 23.0 31.1 1 3 4 20.3 31.3 1 3 5 25.5 31.4 1 4 1 19.6 27.4
1 4 2 19.8 25.9 1 4 3 22.2 27.3 1 4 4 19.5 28.5 1 4 5 19.6 28.1
2 1 1 18.0 28.0 2 1 2 19.6 28.4 2 1 3 19.3 30.6 2 1 4 18.0 30.0
2 1 5 20.1 30.3 2 2 1 24.0 38.8 2 2 2 23.8 37.4 2 2 3 24.2 36.9
2 2 4 24.2 38.9 2 2 5 27.8 37.0 2 3 1 25.6 34.7 2 3 2 23.4 34.0
2 3 3 23.7 35.7 2 3 4 20.6 35.3 2 3 5 26.1 35.9 2 4 1 20.4 32.3
2 4 2 24.6 34.6 2 4 3 23.9 32.8 2 4 4 21.1 34.1 2 4 5 20.0 33.0
3 1 1 18.3 30.1 3 1 2 19.8 31.0 3 1 3 17.6 30.6 3 1 4 17.9 31.9
3 1 5 20.8 32.8 3 2 1 23.4 39.8 3 2 2 23.4 39.4 3 2 3 26.5 41.7
3 2 4 24.4 41.6 3 2 5 27.1 41.3 3 3 1 25.6 36.6 3 3 2 23.5 37.0
3 3 3 23.7 37.9 3 3 4 21.4 38.4 3 3 5 25.5 37.5 3 4 1 17.5 31.5
3 4 2 19.5 31.6 3 4 3 21.7 32.4 3 4 4 18.4 33.4 3 4 5 16.5 31.5
解：SAS程序如下：
options linesize=76;
data example;
infile ‘a:\2-6data.dat’;
input a b c r1 r2 @@;
run;
proc anova;
class a b c;
model r1 r2 = a b c a*b a*c b*c a*b*c;
test h = a e = a*b;
test h = c e = b*c;
test h = a*c e = a*b*c;
means a / duncan e = a*b alpha = 0.01;
means c / lsd e = b*c alpha = 0.01;
run;
与单因素方差分析的SAS程序相比，大同小异。在这里由于因素由1个变为3个，因此分类变量相应变为3个。在MODEL语句中r1 r2 = a b c a*b a*c b*c a*b*c; 的含义是，需要分析a、b、c三个主效应，两两交互作用及三重交互作用对因变量r1和r2的贡献。实际上，这里是两次方差分析，得到两个方差分析表，一个是对r1进行的方差分析，一个是对r2进行的方差分析。当然也可以只计算其中的一部分，如r1 r2 = a b c b*c或r2 = a b c a*b a*b*c 等。
TEST语句中h = a e = a*b 的含义是用A´B交互作用检验A因素效应，即FA ＝MSA / MSAB，另外两个TEST语句含义为FC＝MSC / MSBC，FAC＝MSAC / MSABC。在没有特别说明时，因素的效应都是用MSe检验的（见课本9.5.3）。当然，随着模型的改变，检验统计量会相应改变，这里的TEST语句也要改变。
MEANS语句中选项e = a*b是指明在做DUNCAN检验时，应使用MSAB作为误差均方检验因素A的效应，否则将使用MSe做检验。
实验结果中，若有缺失数据，缺失的数据在方差分析中将被忽略掉，因此实验结果中的数据应完整。
执行上述程序，输出的结果见表2－14。
表2－14 例2.10方差分析输出的结果
The SAS System
Analysis of Variance Procedure
Class Level Information
Class
Levels
Values
A
3
1 2 3
B
4
1 2 3 4
C
5
1 2 3 4 5
Number of observations in data set = 120
The SAS System
Analysis of Variance Procedure
Dependent Variable: R1
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
59
1028.71625
17.43587
35.88
0.0001
Error
60
29.15500
0.48592
Correted Total
119
1057.87125
R-Square
C.V.
Root MSE
R1 Mean
0.972440
3.199437
0.69708
21.7875
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
21.608000
10.804000
22.23
0.0001
B
3
748.776917
249.592306
513.65
0.0001
C
4
68.006667
17.001667
34.99
0.0001
A*B
6
34.511333
5.751889
11.84
0.0001
A*C
8
6.035333
0.754417
1.55
0.1586
B*C
12
129.352667
10.779389
22.18
0.0001
A*B*C
24
20.425333
0.851056
1.75
0.0412
Tests of Hypotheses using the Anova MS for A*B as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
21.6080000
10.8040000
1.88
0.2326
Tests of Hypotheses using the Anova MS for B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
C
4
68.0066667
17.0016667
1.58
0.2432
Tests of Hypotheses using the Anova MS for A*B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A*C
8
6.03533333
0.75441667
0.89
0.5421
The SAS System
Analysis of Variance Procedure
Dependent Variable: R2
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
59
2224.52967
37.70389
85.85
0.0001
Error
60
26.35000
0.43917
Corrected Total
119
2250.87967
R-Square
C.V.
Root MSE
R2 Mean
0.988293
2.014173
0.66270
32.9017
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
779.20117
389.60058
887.14
0.0001
B
3
1314.66700
438.22233
997.85
0.0001
C
4
38.03300
9.50825
21.65
0.0001
A*B
6
53.47350
8.91225
20.29
0.0001
A*C
8
5.84050
0.73006
1.66
0.1266
B*C
12
7.51300
0.62608
1.43
0.1798
A*B*C
24
25.80150
1.07506
2.45
0.0027
Tests of Hypotheses using the Anova MS for A*B as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A
2
779.201167
389.600583
43.72
0.0003
Tests of Hypotheses using the Anova MS for B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
C
4
38.0330000
9.5082500
15.19
0.0001
Tests of Hypotheses using the Anova MS for A*B*C as an error term
Source
DF
Anova SS
Mean Square
F Value
Pr > F
A*C
8
5.84050000
0.73006250
0.68
0.7052
The SAS System
Analysis of Variance Procedure
Duncan's Multiple Range Test for variable: R1
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha=0.01 df=6 MSE=5.751889
Number of Means
2
3
Critical Range
1.988
2.063
Means with the same letter are not significantly different.
Duncan Grouping
Mean
N
A
A
22.3775
40
2
A
A
21.5875
40
3
A
A
21.3975
40
1
The SAS System
Analysis of Variance Procedure
Duncan's Multiple Range Test for variable: R2
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha=0.01 df=6 MSE=8.91225
Number of Means
2
3
Critical Range
2.475
2.567
Means with the same letter are not significantly different.
Duncan Grouping
Mean
N
A
A
35.3975
40
3
A
A
33.9050
40
2
B
29.4025
40
1
The SAS System
Analysis of Variance Procedure
T tests (LSD) for variable: R1
NOTE: This test controls the type I comparisonwise error rate not
the experimentwise error rate.
Alpha=0.01 df=12 MSE=10.77939
Critical Value of T=3.05
Least Significant Difference=2.895
Means with the same letter are not significantly different.
T Grouping
Mean
N
C
A
22.9083
24
5
A
A
22.2000
24
3
A
A
21.6917
24
2
A
A
21.4958
24
1
A
A
20.6417
24
4
The SAS System
Analysis of Variance Procedure
T tests (LSD) for variable: R2
NOTE: This test controls the type I comparisonwise error rate not
the experimentwise error rate.
Alpha=0.01 df=12 MSE=0.626083
Critical Value of T=3.05
Least Significant Difference= 0.6977
Means with the same letter are not significantly different.
T Grouping
Mean
N
C
A
33.7375
24
4
A
B A
33.1917
24
5
B
B
33.0292
24
3
C
32.2875
24
2
C