# [BioC] Limma contrasts question

Daniel Brewer daniel.brewer at icr.ac.uk
Wed Oct 22 15:50:06 CEST 2008

```
James W. MacDonald wrote:
> 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.
>
> Best,
>
> Jim
>
>
>>
>> Many thanks
>>
>> Dan
>>
>

Thanks for that, that is brilliant and has clarified everything.  I did
a comparison of the controls and there were no significant genes found
which is encouraging.

Many thanks

Dan

--
**************************************************************
Daniel Brewer, Ph.D.

Institute of Cancer Research
Molecular Carcinogenesis
Email: daniel.brewer at icr.ac.uk
**************************************************************

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