Common mistake 1 with Pie chart

Using a pie to compare, which is what readers will try to do.

Common mistake 2 with Pie chart

3-D or exploded pies, which distort the areas further.

Common mistake 3 with Pie chart

Percentages on small samples: 100% of two observations is two observations.

Common mistake 4 with Pie chart

Using a pie for a change over time by showing two of them. The comparison the reader wants is between corresponding slices, and that is precisely the comparison two pies make hardest.

EconStatsCraft › Pie chart

Pie chart

Parts of a single whole. Included because it is asked for, with the caveat attached: people judge angles badly and lengths well, so two similar slices are indistinguishable and bars would answer the same question better.

What it needs

Categories
Amounts

The intuition

A pie chart asks the eye to compare angles, which people do badly - and it usually asks this to convey numbers that would fit in a sentence. It has one genuine strength: the metaphor of a whole being divided is immediate, and for two or three parts where the point is "roughly half" rather than a precise ranking, it communicates faster than a bar chart. Beyond that it is worse at everything.

When to use it

When there are two or three parts, the point really is "these are the parts of one whole", and precision does not matter. In almost every other case bars answer the same question better, and this app says so on the chart.

Where the estimator comes from

Slice i subtends an angle \theta_i=2\pi\,y_i/\sum_j y_j and its area is proportional to the same fraction. The reader must therefore judge either angle or area, and both sit near the bottom of the Cleveland-McGill accuracy ranking - well below the length judgement a bar chart offers for the identical data. The normalisation to a whole also means the chart CANNOT represent anything that does not sum meaningfully: overlapping categories, multiple responses, or negative values have no valid pie.

What it assumes

The parts are mutually exclusive and add to the whole. Overlapping categories make a pie that sums to more than 100% and looks fine.
Everything is non-negative. A negative share is not a slice; the app drops negatives and warns rather than drawing them.
The total is a meaningful quantity. Shares of a total that nobody would ever add up - market shares across unrelated markets - are arithmetic rather than information.
There are few enough slices to label directly. A legend forces the reader to look back and forth, which is where most of the format's difficulty comes from.

Statistical properties

Angle and area are among the least accurately judged visual encodings. The same data as a bar chart is read faster and more accurately, which is the whole case against pies.
Slices close in size cannot be ranked by eye. If the reader needs to know which of two similar categories is larger, the pie actively prevents them from finding out.
It only works when the parts sum to a meaningful whole. Multiple-response survey data, where respondents can pick several options, has no valid pie chart and one is drawn anyway constantly.
Three-dimensional pies distort the areas by perspective, making front slices look larger. There is no defensible use for one.
Beyond about five slices the labels no longer fit and the small slices become indistinguishable. A ranked bar chart handles fifty categories comfortably.
Two pies side by side cannot be compared: the reader must judge changes in angle across two circles, which is harder still. Use a grouped or stacked bar for change in composition.

How to read the output

Only large differences are readable. If two slices are within a few percentage points, the chart cannot tell you which is bigger and the labels are doing all the work.
Comparing two pies is harder still. For change over time use a stacked bar or a slope chart.
Everything past the eleven largest slices is combined into "Other" here, because a pie with thirty slices conveys nothing.
Start the largest slice at twelve o'clock. Angles are read most accurately from the vertical, and the convention exists to make the main comparison the easiest one.

A worked reading

Market shares of 34%, 33% and 33% make a pie in which the leader is genuinely invisible - three slices that look identical, when the ranking is the entire point of the chart. The same three numbers as bars show the difference immediately, and as a sentence they are clearer than either. The pie survives one case: a single share against its complement, where "about a third" is the message and precision is not wanted. If you find yourself adding data labels so the reader can tell the slices apart, the labels are doing the work and the chart is decoration.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Two slices of similar size	Angles cannot be ranked by eye	Use a bar chart if the ranking matters
Slices summing to more than 100%	Multiple-response data	A pie is invalid. Use a bar chart of percentages
Twelve slices	Far beyond readability	Rank as bars, or group the tail
A negative value	No valid representation	Use bars
Two pies compared	Angle comparison across circles	Use a grouped bar
A 3D pie	Perspective distorts the areas	Never defensible

Common mistakes

Using a pie to compare, which is what readers will try to do.
3-D or exploded pies, which distort the areas further.
Percentages on small samples: 100% of two observations is two observations.
Using a pie for a change over time by showing two of them. The comparison the reader wants is between corresponding slices, and that is precisely the comparison two pies make hardest.

Where to read this properly

Cleveland and McGill (1984), JASA 79(387).
Spence and Lewandowsky (1991), "Displaying Proportions and Percentages", Applied Cognitive Psychology 5(1) - a partial defence of pies.
Few, "Save the Pies for Dessert" (2007), Perceptual Edge.

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Pie chart

What it needs

The intuition

When to use it

Where the estimator comes from

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

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