## Misleading Visual for the Day

### March 17, 2007

From Foreign Policy magazine (as posted by The Bayesian Heresy). Without looking at the numbers, predict whether the red or the blue portion is larger:

As the numbers indicate, the red and blue sections should be the same size. Here is what a more accurate (though admittedly less visually pleasing) portrayal of the numbers would look like:

Of course, the relative size of the red and blue sections is not the focus here; the vast difference between them and the size of the yellow section is the important thing. However, extrapolating from the fact that blue looks larger than red despite being the same size, one would guess that yellow appears much larger than it actually should. Indeed, look at my bar chart above and notice that you could fit about 25 red bars (or blue bars) inside the yellow bar, indicating that the expenditures on defense are about 25 times those on training the Iraq Security Forces. Now, look again at the pyramid chart and notice that you could fit many more than 25 of the red sections inside the yellow section.

This is the problem with trying to represent uni-dimensional data in three dimensions. People forget about the effect of volume. It appears whoever created the Foreign Policy chart simply used the dollar amounts to calculate the height of each section, and then expanded those heights into the shape of a pyramid, vastly distorting the resulting impression. Edward Tufte would not be pleased. The Benjamin Franklin picture on the same page is pretty cool though.

As a final, non-graphically-related note, the chart is also problematic for its selective comparison of a few components of the Iraq cost to the remainder. Breaking out only these sections implies that they are much smaller than one would expect relative to the total cost, but that implication may not be warranted if one looked at the breakdown of the rest of the spending (how much on U.S. troop salaries, how much on medical care, how much for various types of equipment?). The cost of "expanding the U.S. Army" is listed as $150 billion. Why isn’t that included on the chart? Focusing on a few statistics and leaving the rest of the data as a monolithic "other" does not provide the complete picture.