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MACROSCOPE

Why Is a Raven Like a Writing Desk?

Musing on the power of convention

Howard Wainer

Pie in the Trash

William%20Playfair%u2019s%20pie%20chartClick to Enlarge ImageIn his 1801 Statistical Breviary, William Playfair, the Scot who invented many forms of statistical graphics, proposed the pie chart. Playfair's pie had but three segments and showed what proportions of the Turkish Empire were in Europe, Asia and Africa. It worked very well. Indeed, to test its efficacy, one can easily demonstrate that a small child can tell that 1/3 is larger than 1/4 from a pie chart far more easily than from the fractions themselves. But since Playfair's time, pie charts have become conventional and thus are often used to display much more complex information, this despite strong evidence that a pie chart's efficacy in such a situation is suspect.

In 1990, the New York Times used a pie very much like the one shown in the first figure to communicate the content of what New Yorkers typically discard. The content is a remarkably apt metaphor for the quality of the plot.

The%20dot%20chartClick to Enlarge ImageWe can tell how much of each component is discarded, but only by reading the amount from the label. Because we must read the graph rather than see it, what value is added by the pictorial representation over the numerical? Concerns such as these led the statistician William Cleveland, in his 1985 book The Elements of Graphing Data, to propose the dot chart as an alternative. He found, through a series of experiments, that humans could visually judge lengths far more accurately than areas or angles. So by transforming the pie segments to line segments punctuated with a large dot, he was able to produce a plot that has, in this instance, substantially better perceptual characteristics than Playfair's pie (second figure). Nevertheless, in the intervening 23 years the popularity of the overmatched pie has not decreased, and, sadly, the use of Cleveland's excellent proposal has seen no substantial increase.

Once again, the reason is convention.

It is natural to ask how long it takes for a genuinely superior product to supplant one that is well established. For the pie chart 20 years is not enough; for the QWERTY keyboard it is 150 years and still counting.




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