双因素方差分析.docx
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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
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