[BioC] ANOVA vs T-TEST vs eBayes

[Simon Anders]

Hi

avehna wrote:
> I'm trying to identify genes that are differentially expressed in 4
> different treatments vs Control. First, I applied
> *pairwise.comparison*(simpleaffy library) to my data, and then, just
> to compare both results, I
> tried *lmFit* and *eBayes* (from limma library). I was wondering which
> method is best, because although  pairwise.comparison applies a t-test, it
> doesn't include Bonferroni correction. On the other hand I'm not sure
> whether fitting the data to a linear model using lmFit and eBayes is more
> convenient. I have also found another library(maanova) that uses Anova and
> it's also suitable for DNA microarray analyzes.

First of all: If you have the trivial linear model of just comparing two 
  conditions against each other, the F test for the coefficient for the 
condition (i.e., the test that ANOVA does) is the same thing as a t 
test. Hence, doing a t test and an ANOVA should give the same results in 
the case of just two conditions.

The main issue with the t test is that the denominator of the 't' value 
is the sample variance, as estimated from the values of the gene in the 
replicates. As you only have four replicates, this estimate may 
fluctuate a lot. What Limma's eBayes does is to "share information 
across genes", i.e., it find a compromise between the variance estimate 
for the gene under consideration and the average variance from all the 
genes. This gives more reliable results.

The correction for multiple testing is a completely separate issue: All 
these techniques give you raw p values which you should correct for 
multiple testing, either with the standard R function 'p.adjust' or with 
Storey's 'qvalue' package. Make sure you understand what this correction 
actually does, i.e., read up on family-wise error rate (FWER) and 
especially false discovery rate (FDR).

Cheers
   Simon


+---
| Dr. Simon Anders, Dipl.-Phys.
| European Molecular Biology Laboratory (EMBL), Heidelberg
| office phone +49-6221-387-8632
| preferred (permanent) e-mail: sanders at fs.tum.de