来自 R 中双向方差分析的单向方差分析数据
我运行了双向方差分析，如果我没记错的话，除了交互作用之外，返回结果还为您提供了每个单独参数的单向分析的 p 值。为什么当我对同一参数进行单独的单向分析时，得到的基因不同？
I ran a two-way ANOVA analysis and if I'm not mistaken, the return also gives you p values for a one way analysis for each separate parameter in addition to the interaction. Why is it that when I do a separate one-way analysis on that same parameter, the resulting genes are different?
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这是因为当您对单个因素进行单向分析时，您会将交互方差和自由度留在残差中。如果您在没有交互的情况下进行加性模型，这也将成立。查看两个方差分析的平方和。效应的 SS 应该总是相同的，但残差的方差以一种方式上升。这并不总是保证添加交互作用会使效果更小，因为交互作用消除的自由度可能无法弥补可变性。
当然，如果没有特定问题的示例，很难判断还发生了什么。您可能还会遇到其他问题，即交叉不完全、N 不均匀以及在删除因子时应聚合的多重采样。
It's because when you do the one way analysis of a single factor you're leaving the interaction variance and degrees of freedom in the residuals. This will also be true if you do the additive model without interactions. Look at the sums of squares of the two ANOVAs. The SS for the effect always should be saying the same but the variance for the residuals goes up in the one way. This doesn't always guarantee that adding the interaction makes your effect smaller because the degrees of freedom removed by the interaction may not make up for the variability.
Of course, without an example of your particular problem it's hard to tell what else is going on. You might have further issues where it's not perfectly crossed, uneven N's, and multiple sampling where you should be aggregating when removing factors.
是的，这是方差分析和回归的正常属性！当您包含新参数时，它会“吃掉”被解释变量的整体可变性中的一些东西，因此其他参数也会受到影响。通过添加新参数，您可以将其从其他参数中“过滤掉”。可能会出现参数a的单向方差分析并不显着的情况，但是一旦在双向方差分析中添加参数b，参数a就会突然变得显着！克劳利的统计计算就是一个很好的例子。
Yes, it is a normal property of ANOVA and regression! When you include new parameter, it will "eat up" something from the overall variability of the explained variable, so that the other parameters are also affected. By adding new parameter you kind of "filter it out" from the other parameters. It might happen that one-way ANOVA for parameter a will not be significant, but once you add parameter b in two-way ANOVA, the parameter a will suddenly become significant! Very good example on this is in Crawley's Statistical Computing.