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

log2(SampleSignalReferenceSignal)

  • This ratio may or may not include background subtraction

log2(SampleSignal−SampleBackgroundReferenceSignal−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

  • log2(xy)=log2(x)−log2(y) - fold change converted to difference
  • log ratios are symmetric around 0
  • log2(1)=0
  • log2(2)=1
  • log2(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