**30**wrote:

**37k**• written 5.5 years ago by Jérôme Lane •

**30**

Question: [limma] [Rfit] [samr] Gene expression distribution using lmFit and eBayes

1

Jérôme Lane • **30** wrote:

Hi,
The 3/4 of my microarray gene expressions have non normal
distribution with
most of p-values after Shapiro test under 10x-5.
I tried linear ranked regression from rfit (no normality assumption
for
residues) from Rfit package for adjustment of covariables + SAM
(non
parametric) from samr package but results where not as biologically
relevant
as lmFit + eBayes could provide.
I know that lmFit function can analyses gene expression not
strictly normal,
but what is the limit ?
Is it statistically relevant to use lmFit + eBayes according to my
data ?
Best regards,
J??r??me Lane

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modified 5.5 years ago
by
Gordon Smyth ♦ **37k**
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written
5.5 years ago by
Jérôme Lane • **30**

Answer: [limma] [Rfit] [samr] Gene expression distribution using lmFit and eBayes

1

5.5 years ago by

Gordon Smyth ♦ **37k**

Walter and Eliza Hall Institute of Medical Research, Melbourne, Australia

Gordon Smyth ♦ **37k** wrote:

Dear Jerome,

The Shapiro test is only applicable to iid samples, so it is difficult to see how it could be used to test normality of expression values in a linear modelling context. If you have applied the test to the normalized expression values for each gene, then I suspect that the test is actually picking up differential expression rather than non-normality.

The limma code is very robust against non-normality. All the usual microarray platforms and standard preprocessing procedures produce data that is normally distributed to a good enough approximation. Much effort has been devoted to developing good preprocessing and normalization algorithms.

The concept of "robustness" in statistical analysis goes back a 1953 paper by George Box in Biometrika. In that paper, Box wrote of the "remarkable property of robustness to non-normality which [tests for comparing means] possess". The tests done by limma inherit the robustness property that Box was referring to. Box made the point that the robustness of the two sample t-test was not improved by checking first for equal variances. He said

*"To make the preliminary test on variances is rather like putting to sea
in a rowing boat to find out whether conditions are sufficiently calm for
an ocean liner to leave port!"*

I rather think that, if Box was still alive today, he might say something similar about a preliminary Shapiro test!

Best wishes Gordon

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