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The mystery of circle visualization


Data visualization is a very important and useful tool during the daily decision making processes. Why? Because the human brain can process the graphs, charts much more easier than spreadsheets or databases. So visual presentations could be very informative if we use them in the right way. There is a lot of reccomendation in connection with the right use of several visualizations, but sometimes these opinions are in conflict with each other.

In this topic we will try to find the answer for a bubble chart related stuff. Bubble chart is a modified version of the simple scatter plot, where you can visualize your numerical data along two angles. In the case of bubble charts we replace the data points with circles  or bubbles with a given size which means an additional dimension. So you can use a third measurement which could give you deeper insights into your data.

The main question of this article is related to this additional dimension: the size of the circle.

If someone asks you to choose a circle which is twice as big as the original, which selection method would you use? You will choose the circle with double area or the other one with double radius? How people identify the size of the circle, based on area or radius? Check out our test, and you will get the answer for the previous questions.

The experiment

I this section we show you, how we tested our users in this research. On the picture below you can see three circles with their appropiate properties. The first one is the reference circle, the second circle has twice bigger area and the last one has twice bigger radius than the reference.


cir_50 cir_70 cir_100
Reference circle Circle with twice area Circle with twice radius
Radius 25 px 35,25 px 50 px
Area 1962,5 3925 7850

In the first phase of the research we had to develope an own enviroment, where the test happened. The technical background is irrelevant, so we don’t want to bore you with it.

During the developement we had the following expectations:

  • The reference circle has to be on the left side.
  • The reference circle do not be too small, so the human eye can sense it easily.
  • On the right side we show 10 circles which have randomly generated properties (position, size, fill). The biggest circle’s radius can not be three times big as the reference circle’s radius.

The second phase was the test phase, when the users picked the circle that they thought right. On the picture below you see the test environment where we gathered the data to the research.



















A user had to pick 100 circles during the test period. The results are shown on the scatter plot below.



There are two gray reference lines which shows:

  • radius is twice as big (y=2x)
  • area is twice as big (y=√2x)

The following comparison illustrates the difference between the two most different data sets. (Click to zoom)


The charts clearly shows that the method of choosing can be completely different

User 4 is usually chosen those circles that had twice as big area than original circles.
User 2 is usually chosen those circles that had twice (or more) as big radius than original circles. (and thus, at least 4-times as big area!)

Final conclusion

If we would like to visualize a quantiative dataset via circles, we have to indicate the method of the drawing to the user. It is important because people thinks differently, so someone thinking based on area, while others thinking based on radius. The area based approach of the circle visualization is a bit comfortable because it results spacious and more attractive visualization.

Several things may influence the thinking of people in that situation. For example: visual effects (distance from the reference circle), logical skills , fields of interest, technical skills…


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