Size matters

In data visualization, size actually matters. Look at the two column charts below:

Imagine the headlines for these two graphs. For the graph on the left, you might read “Health Expenditure in Finland Explodes!”. The graph on the right might come under the headline “Health Expenditure in Finland remains mainly stable”. Now look at the data. It’s the same data presented in two different (incorrect) ways.

In the graph on the left, the data doesn’t start at $0, but somewhere around $3000. This makes the differences appear proportionally much larger – for example, expenditure from 2001-2002 appears to have tripled, at least! In reality, this wasn’t the case. The square aspect ratio (the graph is the same height as width) of the graph further aggravates the effect.

The graph on the right starts with $0 but has a range up to $30,000, even though our data only ranges to $9000. This is more accurate than the graph on the left, but is still confusing. No wonder people think of statistics as lies if they are used to deceive people about data.

This example illustrates how important it is to visualize your data properly. Here are some simple rules:

• Always use a range that is appropriate to your data
• Note it properly on the respective axis!
• The changes in size we see in a chart should actually reflect the change of size in your data. So if your data shows B is 2 times A, then B should be 2 times bigger in your visualization.

The simple “reflect the size” rule becomes even more difficult in 2 dimensions, when you have to worry about the total area. At one point, news outlets started to replace columns with pictures, and then continue to scale the dimensions of pictures up in the old way. The problem? If you adjust the height to reflect the change and the width automatically increases with it, the area increases even more and will become completely wrong! Confused? Look at these bubbles:

Answer: The diagram on the right.

Remember the formula for calculating the area of a circle? (Area = πr² If this doesn’t look familiar, see here). In the left hand diagram, the radius of A (r) was doubled. This means that the total area goes up by a scale factor of four! This is wrong. If B is to represent a number twice the size of A, we need the area of B to be double the area of A. To correctly calculate this, we need to adjust the length of the radius by ⎷2. This gives us a realistic change in size.