5.2 years ago by

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

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
> Date: Thu, 21 Nov 2013 17:42:21 -0500
> From: Jerome Lane <jerome.lane at="" criucpq.ulaval.ca="">
> To: "bioconductor at stat.math.ethz.ch" <bioconductor at="" stat.math.ethz.ch="">
> Subject: [BioC] [limma] [Rfit] [samr] Gene expression distribution
> using lmFit and eBayes
>
> 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,
>
> Jerome Lane
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