## When pictures lie

One of the most improvable characteristics of scientific papers is the graphical presentation of numerical data. It is sad to see that thirty years after Tufte published the first edition of his masterpiece [1] many authors are still including grossly inaccurate graphics. Sadder still when the authors are professional graphists, who should know better. Take this chart [2] from the last newsletter of Migros, Switzerland’s largest supermarket chain. To convince Swiss people that they should not worry about their food bills, it displays the ratio of food expenses to revenue in various countries. There would be many good ways to represent this information graphically, but someone thought it clever to draw variable-size coins of the respective currencies. According to the text, “*the bigger the circle, the larger the income’s share devoted to food*“.

Just a minor problem: the visual effect is utterly misleading. Taking three examples from the numbers given, the ratio is roughly 10% for Switzerland, 30% for Russia, 40% for Morocco. And, sure enough, compared to the Swiss coin in the figure, the Russian coin is about three times bigger and the Moroccan coin four times… in *diameter*! What the eye sees, of course, is the *area*. Since the area varies as the square of the diameter, one gets the impression that Russians spend *nine* times, not three, and Moroccans *sixteen* times, not four, as much as the Swiss.

To convey the correct suggestion, the diameter of the Russian coin should have been about 73% larger than the Swiss coin’s diameter (the square root of three is about 1.73) , and the diameter of the Moroccan coin twice larger, that is to say half of what it is.

The impression is particularly misleading for countries where the ratio, unlike in Russia or Morocco, is close to Switzerland’s. Most interestingly, although no doubt by accident, for neighboring countries, where Swiss people are prone to go shopping in search of a bargain, a practice that possibly does not enthuse Migros. The extra percentage devoted to food (using this time no longer rough approximations but precise values from the figures given in the Migros page) is 4% for Austria (10.9 ratio vs Switzerland’s 10.2), 8% for Germany (11.1), 30% for France (13.3) and 43% for Italy (14.6). But if you look at the picture the circles suggest much bigger differences; for example the Italian circle is obviously computed from the ratio of the squares, 14.6^{2} / 10.6^{2}, showing an increase of 104%. In other words, Italians proportionally devote to food a little over two-fifths more than the Swiss, but the graph suggests they spend *twice as much*.

On the premise that one should not ascribe to malevolence what can be explained by ignorance, I hope the Migros graphists will get a copy of Tufte’s book for their future endeavors.

Read Tufte too if you want the pictures in your papers to be not just attractive but accurate.

#### References

[1] Edward R. Tufte: *The Visual Display of Quantitative Information*, Graphics Press, second edition, 2001. See his site here.

[2] “*How much do we spend to feed ourselves?*” on the Migros site, available here for the French version (replace “fr” in the URL by “de” for German and “it” for Italian, I did not see an English version). Click on the figure for a readable version.