双因素方差分析.docx
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双因素方差分析
5.某企业在制定某商品的广告策略时，收集了该商品在不同地区采用不同广告形式促销后的销售额数据，希望对广告形式和地区是否对商品销售额产生影响进行分析，
a）以商品销售额为因变量，广告形式和地区为自变量，通过单因素方差分析方法分别对广告形式、地区对销售额的影响进行分析；
b）试进一步分析，究竟哪种广告形式的作用较明显，哪种不明显，以及销售额和地区之间的关系等。
c）试分析广告形式、地区以及两者的交互作用是否对商品销售额产生影响。
（数据见练习2数据.xls—练习2.5，其中广告形式为：
1.报纸；2.广播；3.宣传品；4.体验）
答：
（a）
以广告形式为自变量时，
广告形式对销售额没有差异
：
广告形式对销售额有差异
0.05
通过SPSS分析可以得到下面的结论
F分布值为2.6693
本题所计算的结果13.483>2.6693
决策：
拒绝
结论：
有显著证据表明，广告形式对销售额有显著差异
以地区为自变量时
:
地区对销售额没有影响
：
地区对销售额有影响
构造检验统计量
将数据导入SPSS进行单因素相关性分析
F分布值为1.7044
因为F>P=1.704
决策：
拒绝
结论：
有显著证据表明，地区对销售额有影响
b）
（
）
下面计算广告形式的影响
主要通过LSD来比较
使用matlab计算t分布值为：
>>tinv（0.025,140）
ans=-1.9771
现在构造假设检验量：
提出假设：
:
第i中广告形式的和第j种广告形式对销量没有显著性差异
：
第i中广告形式的和第j种广告形式对销量有显著性差异
结论：
第1种广告形式和第2种广告形式的销量没有显著差异
第1种广告形式和第3种广告形式的销量有显著差异
第1种广告形式和第4种广告形式的销量有显著差异
第2种广告形式和第3种广告形式的销量有显著差异
第2种广告形式和第4种广告形式的销量没有显著差异
第3种广告形式和第4种广告形式的销量有显著差异
而且从均值图分析可以看出来，第1种广告形式对增加销量影响显著，第3种对于减少销量影响显著。
（
）下面分析区域对于销量的影响
提出假设：
:
第i区域的和第j区域对销量没有显著性差异
：
第i区域和第j区域对销量有显著性差异
显著性水平为95%
自由度为126
>>tinv（0.025,126）
ans=-1.9790
LSD=1.979*
决策：
当|
|>LSD时，拒绝
当|
|使用SPSS软件的LSD分析可以得到下表
多重比较
因变量:
VAR00015
LSD
（I）VAR00011
（J）VAR00011
均值差（I-J）
标准误
显著性
95%置信区间
下限
上限
1.00
2.00
-4.37500
5.79135
.451
-15.8359
7.0859
3.00
-21.00000*
5.79135
.000
-32.4609
-9.5391
4.00
-19.25000*
5.79135
.001
-30.7109
-7.7891
5.00
-12.62500*
5.79135
.031
-24.0859
-1.1641
6.00
-6.37500
5.79135
.273
-17.8359
5.0859
7.00
1.25000
5.79135
.829
-10.2109
12.7109
8.00
-13.37500*
5.79135
.023
-24.8359
-1.9141
9.00
2.37500
5.79135
.682
-9.0859
13.8359
10.00
-17.75000*
5.79135
.003
-29.2109
-6.2891
11.00
7.75000
5.79135
.183
-3.7109
19.2109
12.00
-9.75000
5.79135
.095
-21.2109
1.7109
13.00
-7.00000
5.79135
.229
-18.4609
4.4609
14.00
-4.12500
5.79135
.478
-15.5859
7.3359
15.00
-7.00000
5.79135
.229
-18.4609
4.4609
16.00
-9.25000
5.79135
.113
-20.7109
2.2109
17.00
6.12500
5.79135
.292
-5.3359
17.5859
18.00
-8.37500
5.79135
.151
-19.8359
3.0859
2.00
1.00
4.37500
5.79135
.451
-7.0859
15.8359
3.00
-16.62500*
5.79135
.005
-28.0859
-5.1641
4.00
-14.87500*
5.79135
.011
-26.3359
-3.4141
5.00
-8.25000
5.79135
.157
-19.7109
3.2109
6.00
-2.00000
5.79135
.730
-13.4609
9.4609
7.00
5.62500
5.79135
.333
-5.8359
17.0859
8.00
-9.00000
5.79135
.123
-20.4609
2.4609
9.00
6.75000
5.79135
.246
-4.7109
18.2109
10.00
-13.37500*
5.79135
.023
-24.8359
-1.9141
11.00
12.12500*
5.79135
.038
.6641
23.5859
12.00
-5.37500
5.79135
.355
-16.8359
6.0859
13.00
-2.62500
5.79135
.651
-14.0859
8.8359
14.00
.25000
5.79135
.966
-11.2109
11.7109
15.00
-2.62500
5.79135
.651
-14.0859
8.8359
16.00
-4.87500
5.79135
.402
-16.3359
6.5859
17.00
10.50000
5.79135
.072
-.9609
21.9609
18.00
-4.00000
5.79135
.491
-15.4609
7.4609
3.00
1.00
21.00000*
5.79135
.000
9.5391
32.4609
2.00
16.62500*
5.79135
.005
5.1641
28.0859
4.00
1.75000
5.79135
.763
-9.7109
13.2109
5.00
8.37500
5.79135
.151
-3.0859
19.8359
6.00
14.62500*
5.79135
.013
3.1641
26.0859
7.00
22.25000*
5.79135
.000
10.7891
33.7109
8.00
7.62500
5.79135
.190
-3.8359
19.0859
9.00
23.37500*
5.79135
.000
11.9141
34.8359
10.00
3.25000
5.79135
.576
-8.2109
14.7109
11.00
28.75000*
5.79135
.000
17.2891
40.2109
12.00
11.25000
5.79135
.054
-.2109
22.7109
13.00
14.00000*
5.79135
.017
2.5391
25.4609
14.00
16.87500*
5.79135
.004
5.4141
28.3359
15.00
14.00000*
5.79135
.017
2.5391
25.4609
16.00
11.75000*
5.79135
.045
.2891
23.2109
17.00
27.12500*
5.79135
.000
15.6641
38.5859
18.00
12.62500*
5.79135
.031
1.1641
24.0859
4.00
1.00
19.25000*
5.79135
.001
7.7891
30.7109
2.00
14.87500*
5.79135
.011
3.4141
26.3359
3.00
-1.75000
5.79135
.763
-13.2109
9.7109
5.00
6.62500
5.79135
.255
-4.8359
18.0859
6.00
12.87500*
5.79135
.028
1.4141
24.3359
7.00
20.50000*
5.79135
.001
9.0391
31.9609
8.00
5.87500
5.79135
.312
-5.5859
17.3359
9.00
21.62500*
5.79135
.000
10.1641
33.0859
10.00
1.50000
5.79135
.796
-9.9609
12.9609
11.00
27.00000*
5.79135
.000
15.5391
38.4609
12.00
9.50000
5.79135
.103
-1.9609
20.9609
13.00
12.25000*
5.79135
.036
.7891
23.7109
14.00
15.12500*
5.79135
.010
3.6641
26.5859
15.00
12.25000*
5.79135
.036
.7891
23.7109
16.00
10.00000
5.79135
.087
-1.4609
21.4609
17.00
25.37500*
5.79135
.000
13.9141
36.8359
18.00
10.87500
5.79135
.063
-.5859
22.3359
5.00
1.00
12.62500*
5.79135
.031
1.1641
24.0859
2.00
8.25000
5.79135
.157
-3.2109
19.7109
3.00
-8.37500
5.79135
.151
-19.8359
3.0859
4.00
-6.62500
5.79135
.255
-18.0859
4.8359
6.00
6.25000
5.79135
.283
-5.2109
17.7109
7.00
13.87500*
5.79135
.018
2.4141
25.3359
8.00
-.75000
5.79135
.897
-12.2109
10.7109
9.00
15.00000*
5.79135
.011
3.5391
26.4609
10.00
-5.12500
5.79135
.378
-16.5859
6.3359
11.00
20.37500*
5.79135
.001
8.9141
31.8359
12.00
2.87500
5.79135
.620
-8.5859
14.3359
13.00
5.62500
5.79135
.333
-5.8359
17.0859
14.00
8.50000
5.79135
.145
-2.9609
19.9609
15.00
5.62500
5.79135
.333
-5.8359
17.0859
16.00
3.37500
5.79135
.561
-8.0859
14.8359
17.00
18.75000*
5.79135
.002
7.2891
30.2109
18.00
4.25000
5.79135
.464
-7.2109
15.7109
6.00
1.00
6.37500
5.79135
.273
-5.0859
17.8359
2.00
2.00000
5.79135
.730
-9.4609
13.4609
3.00
-14.62500*
5.79135
.013
-26.0859
-3.1641
4.00
-12.87500*
5.79135
.028
-24.3359
-1.4141
5.00
-6.25000
5.79135
.283
-17.7109
5.2109
7.00
7.62500
5.79135
.190
-3.8359
19.0859
8.00
-7.00000
5.79135
.229
-18.4609
4.4609
9.00
8.75000
5.79135
.133
-2.7109
20.2109
10.00
-11.37500
5.79135
.052
-22.8359
.0859
11.00
14.12500*
5.79135
.016
2.6641
25.5859
12.00
-3.37500
5.79135
.561
-14.8359
8.0859
13.00
-.62500
5.79135
.914
-12.0859
10.8359
14.00
2.25000
5.79135
.698
-9.2109
13.7109
15.00
-.62500
5.79135
.914
-12.0859
10.8359
16.00
-2.87500
5.79135
.620
-14.3359
8.5859
17.00
12.50000*
5.79135
.033
1.0391
23.9609
18.00
-2.00000
5.79135
.730
-13.4609
9.4609
7.00
1.00
-1.25000
5.79135
.829
-12.7109
10.2109
2.00
-5.62500
5.79135
.333
-17.0859
5.8359
3.00
-22.25000*
5.79135
.000
-33.7109
-10.7891
4.00
-20.50000*
5.79135
.001
-31.9609
-9.0391
5.00
-13.87500*
5.79135
.018
-25.3359
-2.4141
6.00
-7.62500
5.79135
.190
-19.0859
3.8359
8.00
-14.62500*
5.79135
.013
-26.0859
-3.1641
9.00
1.12500
5.79135
.846
-10.3359
12.5859
10.00
-19.00000*
5.79135
.001
-30.4609
-7.5391
11.00
6.50000
5.79135
.264
-4.9609
17.9609
12.00
-11.00000
5.79135
.060
-22.4609
.4609
13.00
-8.25000
5.79135
.157
-19.7109
3.2109
14.00
-5.37500
5.79135
.355
-16.8359
6.0859
15.00
-8.25000
5.79135
.157
-19.7109
3.2109
16.00
-10.50000
5.79135
.072
-21.9609
.9609
17.00
4.87500
5.79135
.402
-6.5859
16.3359
18.00
-9.62500
5.79135
.099
-21.0859
1.8359
8.00
1.00
13.37500*
5.79135
.023
1.9141
24.8359
2.00
9.00000
5.79135
.123
-2.4609
20.4609
3.00
-7.62500
5.79135
.190
-19.0859
3.8359
4.00
-5.87500
5.79135
.312
-17.3359
5.5859
5.00
.75000
5.79135
.897
-10.7109
12.2109
6.00
7.00000
5.79135
.229
-4.4609
18.4609
7.00
14.62500*
5.79135
.013
3.1641
26.0859
9.00
15.75000*
5.79135
.007
4.2891
27.2109
10.00
-4.37500
5.79135
.451
-15.8359
7.0859
11.00
21.12500*
5.79135
.000
9.6641
32.5859
12.00
3.62500
5.79135
.532
-7.8359
15.0859
13.00
6.37500
5.79135
.273
-5.0859
17.8359
14.00
9.25000
5.79135
.113
-2.2109
20.7109
15.00
6.37500
5.79135
.273
-5.0859
17.8359
16.00
4.12500
5.79135
.478
-7.3359
15.5859
17.00
19.50000*
5.79135
.001
8.0391
30.9609
18.00
5.00000
5.79135
.390
-6.4609
16.4609
9.00
1.00
-2.37500
5.79135
.682
-13.8359
9.0859
2.00
-6.75000
5.79135
.246
-18.2109
4.7109
3.00
-23.37500*
5.79135
.000
-34.8359
-11.9141
4.00
-21.62500*
5.79135
.000
-33.0859
-10.1641
5.00
-15.00000*
5.79135
.011
-26.4609
-3.5391
6.00
-8.75000
5.79135
.133
-20.2109
2.7109
7.00
-1.12500
5.79135
.846
-12.5859
10.3359
8.00
-15.75000*
5.79135
.007
-27.2109
-4.2891
10.00
-20.12500*
5.79135
.001
-31.5859
-8.6641
11.00
5.37500
5.79135
.355
-6.0859
16.8359
12.00
-12.12500*
5.79135
.038
-23.5859
-.6641
13.00
-9.37500
5.79135
.108
-20.8359
2.0859
14.00
-6.50000
5.79135
.264
-17.9609
4.9609
15.00
-9.37500
5.79135
.108
-20.8359
2.0859
16.00
-11.62500*
5.79135
.047
-23.0859
-.1641
17.00
3.75000
5.79135
.518
-7.7109
15.2109
18.00
-10.75000
5.79135
.066
-22.2109
.7109
10.00
1.00
17.75000*
5.79135
.003
6.2891
29.2109
2.00
13.37500*
5.79135
.023
1.9141
24.8359
3.00
-3.25000
5.79135
.576
-14.7109
8.2109
4.00
-1.50000
5.79135
.796
-12.9609
9.9609
5.00
5.12500
5.79135
.378
-6.3359
16.5859
6.00
11.37500
5.79135
.052
-.0859
22.8359
7.00
19.00000*
5.79135
.001
7.5391
30.4609
8.00
4.37500
5.79135
.451
-7.0859
15.8359
9.00
20.12500*
5.79135
.001
8.6641
31.5859
11.00
25.50000*
5.79135
.000
14.0391
36.9609
12.00
8.00000
5.79135
.170
-3.4609
19.4609
13.00
10.75000
5.79135
.066
-.7109
22.2109
14.00
13.62500*
5.79135
.020
2.1641
25.0859
15.00
10.75000
5.79135
.066
-.7109
22.2109
16.00
8.50000
5.79135
.145
-2.9609
19.9609
17.00
23.87500*
5.79135
.000
12.4141
35.3359
18.00
9.37500
5.79135
.108
-2.0859
20.8359
11.00
1.00
-7.75000
5.79135
.183
-19.2109
3.7109
2.00
-12.12500*
5.79135
.038
-23.5859
-.6641
3.00
-28.75000*
5.79135
.000
-40.2109
-17.2891
4.00
-27.00000*
5.79135
.000
-38.4609
-15.5391
5.00
-20.37500*
5.79135
.0
升级会员 