Quantities that are mostly small
Some measurements describe quantities that are small for most 'individuals' but where a few have much larger vaues. Such quantities are said to have skew distributions.
When scatterplots display such skew quantities, the larger values are well separated, but the small values become clustered very closely together and are often hard to distinguish. One solution is to make the axis for this quantity very long.
Life expectancy and Gross National Income (GNI)
The diagram below was published to show that high life expectancy is associated with high GNI in countries. Because most countries have low GNI but a few countries have very high GNI, it is difficult to show any detail about what is happening to the poorer countries in the same diagram that is used for the rich countries. The scatterplot was therefore drawn with an extremely long GNI axis.
Nonlinear axis
A better solution is to replace the standard axis for the measurement by a nonlinear axis in which the small values are spaced out more and the high values are compressed. This is particularly justified for economic measurements. For example, the difference between the GDP per capita of two poor countries, $300 and $600, is equally important as a difference between $30,000 and $60,000 for two rich countries. A nonlinear logarithmic scale spaces out the two poor countries exactly the same as the two rich countries.
Scatterplots with nonlinear axes are harder to understand, so they should only be used in publications where the readers are likely to cope.
Life expectancy and Gross National Income (GNI)
The next scatterplot is similar to the one above, but uses the GNI of the countries in 2006.
Half of the countries had GNI per capita below $6,500 in 2006 and the standard scatterplot groups the poorest countries so close to the left that it is hard to distinguish them.
Drag the slider to the right to make the scale for GNI into a nonlinear logarithmic scale. Observe how the low values of GNI are spaced out and the high values are compressed. Note that the values 600, 6,000 and 60,000 are equally spaced on the logarithmic scale.
Select Display as circles from the pop-up menu to use circles whose areas are proportional to the populations of the countries.
If you use a logarithmic scale, make sure that you label it clearly as such.