(This is a submission from reader Lawrence Mayes. Thank you Lawrence!)

I came across this unusual graphical representation of the destinations of scholarship students:


[Kaiser here: The charts are hidden inside an annoying Flash app and it seems that the bottom half of the chart is cropped out.]

(the original can be seen here: http://www.ibercampus.eu/-270-000-students-benefitted-from-eu-grants-to-study-or-2076.htm)

The question is: what parameter is used to illustrate the figures? - Line length or angle?

The answer is - line length. But the eye is likely to use the angle as the measure and this is where an error may arise. It's almost an optical illusion - the smaller number of students lie on the circumferences of smaller circles - and a smaller length goes further around the circle. Thus, for example, Turkey attracts about one fifth of those students attracted by Germany but it looks like it's nearer half (45 degrees vs 90 degrees).

(The case of Spain is really bizarre - it looks like it's gone round the circle by over 280 degrees but actually what they've done is to break off the line at 90 degrees and stick the bit they broke off back on the diagram at the left.)

I have never seen this type of 'bar chart' before but it is really misleading.


Long-time readers may remember my discussion of the "race-track graph." (here) The "optical illusion" Lawrence mentions above is well known to any track runner. The inside lanes are shorter than outside lanes, so you stagger the starting positions.


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