'Quantities'

Logarithmic transformation can only be used for data sets consisting of positive values — logarithms are not defined for negative or zero values.

They are therefore particularly useful for quantities — i.e. amounts of something. Examples are:

Indeed, many researchers routinely apply logarithmic transformation to quantity data before analysis.

When are they effective?

Logarithmic transformation does not always have a major effect on the shape of a distribution. Its effect depends on the ratio of the largest to smallest value in the data. For example, the highest GDP on the previous page (USA, $5,452 billion) is over 5,000 times the smallest brain weight (Liberia, $1.075 billion). Since this is greater than 103, we say that the data cover over 3 orders of magnitude.

When a data set covers less than 1 order of magnitude (the biggest value is less than 10 times the smallest value), the effect of a logarithmic transformation is less.

Holiday Home Rental data

The dot plot below shows monthly rentals of 42 holiday houses at a beach resort. The highest value ($5400 per month) is 5.4 times the smallest value ($1000 per month).

Drag the slider to apply a logarithmic transformation. Observe that the transformation makes the distribution a little more symmetric, but the effect is much less than in the previous page.