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同一整体,Stdev(overall)为什么会小于Stdev(within) ?

我一直误以为overall包含了within与between,Stdev(overall)理应大于Stdev(within),但是以下的数据却打破了我的想法,那这三者之间到底是什么关系呢? (每个子组有10个数据,usl =115,Lsl=85)

103.9959455
89.38002135
96.99797575
108.5904857
106.3669907
103.0015658
102.3906901
100.2758448
94.64405357
98.88643537
95.44745147
104.8677225
102.147252
95.8453658
97.01171277
103.9861343
100.0435231
96.87321185
105.0366431
97.96168566
99.88588397
115.6509722
102.4990914
99.85233202
105.651566
99.83951229
101.2325533
100.0247537
97.05072719
95.04523661
104.5179012
100.6606737
105.3379292
103.0287359
98.66748688
101.8168949
95.84718839
101.3862049
89.81464003
103.7645737
92.81049276
99.09570425
93.09921604
99.91520021
93.44726918
96.53520279
101.7659796
98.61107997
102.2723472
97.77162279
97.21648595
101.3076764
103.3168193
100.3389641
94.67586246
96.98691156
101.4726217
93.77063366
110.0691062
90.84857383
94.69349395
90.89804904
98.42726366
106.9583652
109.8916405
102.0115043
98.67024368
93.9398155
93.76409861
104.519542
97.26383644
93.21298795
96.50196525
93.70238504
100.0565285
102.9683529
98.14474965
103.8171151
106.4525233
95.30684848
98.92077083
98.4668791
92.78177121
95.47196639
100.3964128
101.9159915
105.8060069
96.19024125
95.61211867
96.82836604
97.59359057
102.9355375
95.64164744
100.081504
110.5782406
101.3241855
92.33331419
106.1310301
98.00403444
102.4869114

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zhaohui2002 (威望:4) (浙江 杭州) 机械制造 工程师

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本帖最后由 zhaohui2002 于 2011-11-3 22:41 编辑


1/ 回答8#的问题答案貌似不正确,具体参照11#和13#楼
2/ 1#的问题回答的应该说是意思对了,但是把名词和表达式写错了
不是S(overall)=S(within)+S(between),而是SS(overall)=SS(within)+SS(between),
简写就是SST=SSW+SSB(这个式子很熟悉吧)
这里的SS不是标准差,也不是方差,而是变异(整体变异=组间变异+组内变异,这个是ANOVA的基础)
变异具有这种相加的性质,为什么方差或标准差又没有呢?
请注意变异和标准差或者方差之间的区别:变异是所有数据之间的,而标准差是把变异再平均一下,换言之,再除以自由度,这一点,10#的回答是对的,不过就是把一些名词表达错误了,所以方差或标准差就没有了这种可加性。

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