4.3 Logarithmic Transformations

It is not uncommon to find ratio variables with distributions that are skew. While this is not necessarily an issue, certain statistical learning methods assume that variables have fairly symmetric bell-shaped distributions. One transformation typically used by analysts to obtain more symmetric distributions from skewed ones is the logarithmic one.

When a variable has positive values, we can log-transform it. This will shrink or compact the long tails, making them more symmetrical. In addition, it will also convert multiplicative relationships to additive ones. Why? Because of the properties of logarithm: \(log(xy) = log(x) + log(y)\) and \(log(x/y) = log(x) - log(y)\).