Processing math: 100%

log2 transformation

Mikhail Dozmorov

Fall 2016

Expression Summaries: cDNA arrays

For custom spotted arrays, the quantity used for analysis is most often the

$log_2(\frac{SampleSignal}{ReferenceSignal})$

This ratio may or may not include background subtraction

$log_2(\frac{SampleSignal-SampleBackground}{ReferenceSignal-ReferenceBackground})$

Problems with fold change

Fold changes, or ratios, can be larger than 1 (2-fold increase), or smaller than one (0.5).
Not symmetric around 1

Why log2

$log_2(\frac{x}{y}) = log_2(x)-log_2(y)$ - fold change converted to difference
log ratios are symmetric around 0
$log_2(1) = 0$
$log_2(2) = 1$
$log_2(0.5) = -1$

log2 transformation

Condition	Fold change	Difference
B vs. A	10	900
C vs. B	10	9000
C vs. A	100	9900

log2 transformation

Note that on a log scale,
The differences are 1.

log2-transformation of raw intensities

The fold change distribution has a fat right tail
The log2-transformed fold changes are linear