'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 mammal brain weight on the previous page (African elephant, 5712 g) is over 40,000 times the smallest brain weight (Lesser short-tailed shrew, 0.14 g). Since this is greater than 104, we say that the data cover over 4 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.
Strength data
The dot plot below shows the 'maximum voluntary isometric strength' (MVIS) of a group of Hong Kong students. The highest value (54 kg) is 5.4 times the smallest value (10 kg).
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.