Note: this is an answer to: general question about homogeneity of variances between microarray groups

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 variances.

George Box had a few choice words more than half a century ago for what you propose, in a famous paper in Biometrika in 1953.  He said it was like setting out  to sea in a rowing boat to check if the weather was calm enough for an ocean liner to leave port.

> 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 arrayWeights() are much better than switching to another type of test, if you really did have a meaningful difference in variabilities between groups.

Best wishes
Gordon

> thak you for any tips
> Best
> Guido