[BioC] Limma contrasts question

James W. MacDonald jmacdon at med.umich.edu
Wed Oct 22 15:07:16 CEST 2008

Daniel Brewer wrote:

> Hi Jim,
> Could you go into the maths of the contrast formulas a bit?  I would
> like to get a really solid understanding of what it is doing for future
> analyses.

Once you understand what the coefficients are, the contrasts are just 
simple algebra. In your case, all of the coefficients are estimating the 
difference between the sample and PC3M (e.g., Knockdown - PC3M).

So the algebra is something like this:

2(Knockdown - PC3M) - (Scramble - PC3M)
2Knockdown - 2PC3M - Scramble + PC3M
2Knockdown - Scramble - PC3M
Knockdown - (Scramble + PC3M)/2

Which is knockdown minus the mean of the controls.

Note that this will be the numerator of the resulting t-statistic. The 
denominator will be sort of an average of the variability within each of 
the three groups being compared. So the question being answered is 'What 
genes are different in Knockdown as compared to the average of the 
controls?'. However, there is nothing here to test if the two controls 
are similar at all (and you might not care).

So for instance, you might have a gene with average expression like this:

Knockdown = 10
PC3M = 4
Scramble = 7

If the intra-group variability is small for each sample type, then you 
will likely get a significant t-statistic even though the two controls 
are probably significantly different as well. Which is why I mentioned 
earlier that you might want to test the Scramble - PC3M contrast as well.



> Many thanks
> Dan

James W. MacDonald, M.S.
Hildebrandt Lab
1150 W. Medical Center Drive
Ann Arbor MI 48109-0646

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