Changes on the log scale

Changes on the log scale can be tricky. But are common. Microarray genetic expression data is commonly observed (immediately transformed) onto the log2 scale.

This makes comparisons on a rate basis, a multiplicative change rather than an additive (think natural logging your outcome in regression and what happens when you take the exponential of both sides to get it back on the original scale – what happens to the right hand side).

log2 has a nice property that a double (on the original scale) is a difference of 1 on the log2 scale. Try it and see. Remember log(b) – log(a) = log(b/a). So if we want to see a doubling of effect (one mean twice the other, 2a=b for example), then we are looking for log2(2), which =1.

This is very helpful for things like power calculations. So if you are looking for a doubling affect (on the raw scale) of data that is being analsysed (on the log2) scale), then you are looking for a mean difference of 1 (in the transformed data – which is on the log2 scale.)

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