SPSS - 方差分析中模型的轻微变化导致平方和发生根本性变化？
我注意到，即使对我的模型进行最轻微的调整，我的模型中的平方和也会发生相当大的变化？？？这正常吗？？？？我使用的是 SPSS 16，下面介绍的两个模型都使用相同的数据和变量，只有一个小变化 - 将其中一个变量分类为 2 级或 3 级变量。
详细信息 - 使用 2 x 2 x 6 混合模型方差分析，其中 6 是重复测量，我在组间分析中得到以下结果
------------------------------------------------------------ Source | Type III SS | df | MS | F | Sig ------------------------------------------------------------ intercept | 4086.46 | 1 | 4086.46 | 104.93 | .000 X | 224.61 | 1 | 224.61 | 5.77 | .019 Y | 2.60 | 1 | 2.60 | .07 | .80 X by Y | 19.25 | 1 | 19.25 | .49 | .49 Error | 2570.40 | 66 | 38.95 |
然后，当我使用完全相同的数据但略有不同的模型时，其中变量 Y 有 3 个水平2 个水平我得到以下结果
------------------------------------------------------------ Source | Type III SS | df | MS | F | Sig ------------------------------------------------------------ intercept | 3603.88 | 1 | 3603.88 | 90.89 | .000 X | 171.89 | 1 | 171.89 | 4.34 | .041 Y | 19.23 | 2 | 9.62 | .24 | .79 X by Y | 17.90 | 2 | 17.90 | .80 | .80 Error | 2537.76 | 64 | 39.65 |
我不明白为什么变量 X 会有不同的平方和，仅仅是因为变量 Y 被分为 3 个水平而不是 2 个。组内分析也是如此。
请帮助我理解：D
提前谢谢你
帕特
I have noticed that the sum of squares in my models can change fairly radically with even the slightest adjustment to my models???? Is this normal???? I'm using SPSS 16, and both models presented below used the same data and variables with only one small change - categorizing one of the variables as either a 2 level or 3 level variable.
Details - using a 2 x 2 x 6 mixed model ANOVA with the 6 being the repeated measure i get the following in the between group analysis
------------------------------------------------------------ Source | Type III SS | df | MS | F | Sig ------------------------------------------------------------ intercept | 4086.46 | 1 | 4086.46 | 104.93 | .000 X | 224.61 | 1 | 224.61 | 5.77 | .019 Y | 2.60 | 1 | 2.60 | .07 | .80 X by Y | 19.25 | 1 | 19.25 | .49 | .49 Error | 2570.40 | 66 | 38.95 |
Then, when I use the exact same data but a slightly different model in which variable Y has 3 levels instead of 2 levels I get the following
------------------------------------------------------------ Source | Type III SS | df | MS | F | Sig ------------------------------------------------------------ intercept | 3603.88 | 1 | 3603.88 | 90.89 | .000 X | 171.89 | 1 | 171.89 | 4.34 | .041 Y | 19.23 | 2 | 9.62 | .24 | .79 X by Y | 17.90 | 2 | 17.90 | .80 | .80 Error | 2537.76 | 64 | 39.65 |
I don't understand why variable X would have a different sum of squares simply because variable Y gets devided up into 3 levels instead of 2. This is also the case in the within groups analysis too.
Please help me understand :D
Thank you in advance
Pat
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X 的 III 型平方和告诉您，当您将 X 添加到包含所有其他项的模型中时，您会获得多少收益。看来 3 水平 Y 变量是比 2 水平变量更好的预测变量：它的 SS 从 2.6 变为 19.23。 （例如，如果 Y 的效果是二次的，则可能会发生这种情况：顶点处的切割不是很有预测性，但切割成三组会更好）。因此，X 需要解释的内容就更少了——它的 SS 降低了。
The type III Sum-of-Squares for X tells you how much you gain when you add X to a model including all the other terms. It appears that the 3-level Y variable is a much better predictor than the 2-level one: its SS went from 2.6 to 19.23. (this can happen, for example, if the effect of Y is quadratic: a cut at the vertex is not very predictive, but cutting into three groups would be better). Thus there is less left for X to explain - its SS decreases.
只是补充一下 Aniko 所说的，变量 X 具有不同平方和的原因仅仅是因为变量 Y 被分为 3 个级别而不是 2 个级别，是因为每个因子的 SS 公式取决于每个处理中的样本数量。当您更改一个因子的水平数时，您实际上更改了每种处理的样本数，这会对所有其他因子的 SS 值产生影响。
Just adding to what Aniko has said, the reason why variable X has a different sum of squares simply because variable Y gets divided up into 3 levels instead of 2, is that the SS formula for each factor depends on the number of samples in each treatment. When you change the number of levels in one factor, you actually change the number of samples for each treatment and this has an impact on the SS value for all the other factors.