Dear Avinash,
Briefly, you have used
design <- model.matrix(~0+Group)
when you needed
design <- model.matrix(~Group)
However, I do not recommend a limma analysis of RPKM values, because it does not respect the mean-variance relationship inherent in the count data. Nicole Cloonan's excellent Nature Methods paper was written four years ago, and our understanding of the statistical analysis RNA-Seq data has moved on considerably since then. Please see the last case study in the limma User's Guide, which analyses the Nigerian HapMap data, for how I recommend limma be used to analyse RNA-Seq data.
Best wishes
Gordon
PS. This answer was originally posted 4 December 2011: Limma - RNA-Seq DE genes - Quantile normalized log transformed RPKM data
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