bars and pies for proportions

Much is said about the relative merits of bars and circles for showing proportions.

All five of these studies legitimize the use of pie charts when conveying proportions and some even show their superiority over bar charts.

I did not encounter any studies that said we should not use pie charts for showing proportions in all cases.

Eells (7) was among the first to publish a paper on this topic in 1926. In his time, pie charts were ridiculed much as they are today for their assumed perceptual inadequacies. For example, he was told that the human eye cannot judge arcs, angles or chords very efficiently.

Eells gave a psychology class two worksheets — a series of pie charts and bar charts — and asked them to estimate the proportion of each segment to the whole.

He also wanted to know more about how circles were processed. So he handed out worksheets to a psychology class and asked them to estimate the proportions in these pie and bar charts.

Not only did he find that pie charts were read as easily, quickly and accurately as bar charts, but that as the number of components in the chart increased, bars become less efficient encoding the data. The opposite was true for pie charts

The three ways participants in Eells’s study reported perceiving proportion in pie charts. Only one woman reported using chords, most likely because she had special training for this. She was the most accurate person in the class in perceiving proportion in pie charts.

He found that 50 percent of people use the outer arc to make proportional judgments, while 25 percent use area, and the other 25 percent use the inner arc or angle. Furthermore, 71 people in the class preferred the pies and only 25 preferred the bars.

He concluded that we ought to use pie charts, not just for their appeal but because of their scientific accuracy.

He also concluded that men were superior to women in estimating these proportions. So, hats off to men… You’ve done it again! (To be clear, that was sarcasm, and Eells’s claim is absurd and sexist. But it is worth calling out this example of casual, institutional bias to acknowledge the ongoing, disproportionate hurdles women must traverse to be accepted as equal in intelligence and abilities to men.)

Eells’s absurd, sexist conclusion from his study.

A follow-up study in response to Eells’s work the following year by Croxton (8) did not find that pie charts were so conclusively better than bar charts, but they did pull ahead for some of the cases.

Six decades later, and in three more experiments, pie charts were hailed for their strength in conveying proportional data, in some way or another.

Simkin and Hastie (9) had participants make proportional judgments and segment-to-segment (comparison) judgments. And found that for segment-to-segment judgments, simple bar charts worked best, followed by divided bar charts and then pie charts.

Simkin and Hastie concluded that individuals have a particular schema for what to expect when viewing a particular chart.

For proportional judgments, pie charts and divided bar charts were tied, with simple bar charts the least effective.

Spence and Lewandowsky (10) found that comparisons among multiple segments take longer and have lower accuracy. Pie charts fared the worst except when multiple segments had to be compared. Tables were found to be inferior to everything except for communicating absolute values, despite what Tufte advises.

Hollands and Spence (11) found that as the number of components in bar charts increase, their effectiveness at communicating proportions decreases. In fact, for each new component in bar charts, a reader needs an additional 1.7 seconds for processing.