# [BioC] Paired arrays and limma

James W. MacDonald jmacdon at med.umich.edu
Wed Mar 12 15:59:21 CET 2008

```Hi John,

john seers (IFR) wrote:
>
>
> Hi James
>
> A fortuitous coincidence you mention my name in a posting when I was
> directly.
>
> The thread in question is:
>
>
> https://stat.ethz.ch/pipermail/bioconductor/2007-November/020291.html
>
>
> I followed the thread through and found it did not offer a solution and
> you finish with:
>
> "I'm not sure why you would want to do things pair-wise, but if you
> really want paired t-tests, then you will have to analyze the data in
> pairs rather than all at once."
>
> I am using limma on a similar setup and I am not sure how to pair the
> data. The setup is before and after two diets and a condition control
> and disease. (There is a section in the limma manual on paired data and
> a section on factorial designs but I am not sure how to marry them).
>
> Can you explain what you mean by "analyzing the data in pairs rather
> than all at once"?

Well, the poster wanted his data to agree with the results from a paired
t-test, which won't happen if you fit a model to all the data and then
compute contrasts. This is because the denominator of the statistic will
be different in the two cases.

In the former, the denominator will be the standard error of the mean,
which is computed using only the two samples under consideration.

In the latter, it will be the sums of squares of error (or some variant
thereof, depending on the model), which measures the within-group
variance of all the groups in the model, not just the two under
consideration for a given contrast.

I didn't know why he would want to do things pair-wise, as the variance
estimates get better as n goes up, so the linear model approach is often
preferable. You can see that in his example - the t-statistic was larger
when he used all his data than when he just used the paired data.

>
> My solution so far is to preprocess the data and take the ratio of the
> expression values of the paired arrays (so halving the number of
> columns) and analyzing them in limma. That removes the pairing from the
> limma analysis. Does that make sense to you?

Well, if by 'take the ratio' you mean 'compute the difference'(we _are_
on the log scale?), then this is essentially what you would be doing by
fitting a batch effect anyway. However, it will limit the types of
comparisons you can make since you are combining the paired data into
differences.

Best,

Jim

>
> Thank you in advance for any time you take.
>
> Regards
>
>
> John Seers
>
>
>
> ---
>
> Web sites:
>
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--
James W. MacDonald, M.S.
Biostatistician
Affymetrix and cDNA Microarray Core
University of Michigan Cancer Center
1500 E. Medical Center Drive
7410 CCGC
Ann Arbor MI 48109
734-647-5623

```