# [BioC] Calculation of t-tests for factorial design

Pascal Gellert pascal.gellert at mpi-bn.mpg.de
Fri Sep 10 16:04:12 CEST 2010

```Hi all,

Unfortunately I cannot find out how limma calculates t-tests for my
factorial design of micrarrays, but let's begin from the start:

I have the following microarray experiment:

WT    Knock-Out
Treated        2    2
Untreated        2    2

This way I can make the following comparisons:

WT Treated / WT Untreated: This shows me, what the effect of the
treatment itself is.
Knock-out Treated / Knock-out Untreated: To see what effect the
treatment has on Knock out animals.
(Knock-out Treated / Knock-out Untreated) / (WT Treated / WT Untreated):
The effect of treatment to Knock-Out animals under consideration of
changes of gene expression due to treatment in WT animals.

So my main interest lies in the last comparison. I did this with the
following code:

row.names=1, as.is=T)
TS <- paste(targets\$Strain, targets\$Treatment, sep=".")
TS <- factor(TS, levels=c("wt.non","ko.non","wt.treat","ko.treat"))

design <- model.matrix(~0+TS)
colnames(design) <- levels(TS)
fit <- lmFit(eset, design)

cont.matrix <- makeContrasts(
WT.nonVStreat =wt.non-wt.treat,
KO.nonVStreat=ko.non-ko.treat,
Diff=(ko.non-ko.treat)-(wt.non-wt.treat),
levels=design)
fit2 <- contrasts.fit(fit, cont.matrix)
fit2 <- eBayes(fit2)

eset contains my expression values in log2 scale.
The contrast are calculated by
wt.non-wt.treat
ko.non-ko.treat
(ko.non-ko.treat)-(wt.non-wt.treat)
as I described above. For all 3 comparisons, eBayes calculates t-tests,
but for the last comparison, which values are used for the t-test?
All signals of ko.non and ko.treat compared to wt.non and wt.treat? I
think it's calculated in a completely different way, does anyone know how?

Best regards,

Pascal

```