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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?

Tot Zam
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John
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  • Can you provide a reproducible example of what you are talking about? – Chase Jul 22 '11 at 16:19
  • Did you mean something like this? utils::data(npk, package="MASS"); summary(aov(yield ~ N*P, npk) ); summary(aov(yield ~ N, npk) ) – EDi Jul 22 '11 at 16:41
  • A reproducible example would be lovely ... http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example – Ben Bolker Jul 25 '11 at 15:30

2 Answers2

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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.

John
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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.

Tomas
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