[BioC] general question about omogeneity of variances between microarray groups

Gordon K Smyth smyth at wehi.EDU.AU
Wed Aug 1 03:46:18 CEST 2012

Dear Guido,

> Date: Tue, 31 Jul 2012 11:13:20 +0200
> From: Guido Leoni <guido.leoni at gmail.com>
> To: <bioconductor at stat.math.ethz.ch>
> Subject: [BioC] general question about omogeneity of variances between
> 	microarray groups
> Dear list
> I'm performing some microarrays analysis for a simple case(15 microarrays)
> , control(3 microarrays) experiment design.
> Don't ask me the reason for which i have a so unbalanced dataset ;-)
> In order to detect differentially expressed genes I wish to perform a LIMMA
> analysis...but checking the omogeneity of variances with bartlett test I
> observ a difference statistically significative between cases and controls.
> According to your experience:
> Is a good idea before doing a parametric analysis checking the variances
> utilizing Bartlett test?

No, it is a very bad idea.  Bartlett's test is well known to be highly 
sensitive to non-normality, so it is very likely to give significant 
results as a result of small deviations from normality rather than genuine 
differences in variances.  By contrast, the two-sided t-test that limma 
does is quite robust against both non-normality and inequality of 

George Box had a few choice words more than half a century ago for what 
you propose.  He said it was like setting out in a rowing boat to 
check if the ocean was calm enough for an ocean liner.  See for example:


> In my case a non parametric test(like SAM) might be better than LIMMA?

As James MacDonald has already said, SAM is not non-parametric and it 
assumes equal variances just like limma.

Even non-parametric tests like the Wilcoxon 2-sample test still assume 
equal variances.

This is not to say that you shouldn't be checking your data.  But 
exploratory methods like plotMDS() are much more relevant than Bartlett's 
test, and solutions like array weights are much better than switching to 
another type of test, if you really did have a meaningful difference in 
variabilities between groups.

Best wishes

> thak you for any tips
> Best
> Guido

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