Common mistake 1 with Bubble chart

Scaling by radius instead of area, which exaggerates large values by squaring them. This app scales area.

Common mistake 2 with Bubble chart

Using size for the outcome. Nobody can read it accurately enough to support a claim.

Common mistake 3 with Bubble chart

Too many bubbles: past a few dozen the chart is an unreadable overlap and a plain scatter is better.

Common mistake 4 with Bubble chart

Encoding a fourth variable as colour as well. Position, size and hue in one chart exceeds what most readers will decode, and the fourth variable usually deserves its own panel.

EconStatsCraft › Bubble chart

Bubble chart

A scatter where the size of each point carries a third variable - the classic cross-country chart. Area is read far less precisely than position, so put the variable you are arguing about on an axis, not in the size.

What it needs

Horizontal variable
Vertical variable

The intuition

A bubble chart is a scatter plot with a third variable encoded as point size. That third channel is far weaker than the two positions it joins - people judge area poorly and inconsistently - so it works for a rough ordering and fails for anything precise. The most common defect is not perceptual but arithmetic: encoding the value as the radius rather than the area, which exaggerates every difference quadratically.

When to use it

When a third variable matters for weighting the reader's attention rather than for measurement: population, firm size, GDP. It says "these observations are not equally important" without pretending to be precise about how much.

Where the estimator comes from

For value v_i the marker must satisfy \text{area}\propto v_i, so the radius is r_i\propto\sqrt{v_i}. Setting r_i\propto v_i instead makes the area proportional to v_i^2: a value twice as large is drawn four times as big. Stevens' power law compounds the problem even when the arithmetic is right - perceived magnitude of an area scales roughly as A^{0.7}, so people systematically UNDER-estimate large circles. The two effects run in opposite directions and do not cancel in any reliable way.

What it assumes

The size variable is non-negative and on a ratio scale, so that twice the value can sensibly mean twice the area.
The size variable is the least important of the three. Area is judged poorly - readers underestimate large circles - so the variable you are arguing about belongs on an axis.
The three variables are on comparable populations. A bubble sized by population and positioned by a per-capita rate mixes stocks and rates, which is legitimate but routinely misread.
The size range is not so wide that small bubbles vanish. When the largest is a thousand times the smallest, area scaling makes the small ones invisible and the chart shows only the big ones.

Statistical properties

Size must encode area, not radius. Radius encoding is a squaring error and is common in spreadsheet defaults.
Even with correct areas, judgement is poor: Cleveland and McGill place area well below length and position. Use size for a rough third dimension, never for the variable the argument rests on.
A size legend is mandatory and must show at least three reference circles, because readers cannot infer the scale from the chart.
Zero and negative values have no valid radius. They are usually drawn as invisible or as a minimum-size dot, both of which mislead.
Overlapping bubbles hide each other. Draw large behind small, and use transparency, or a large bubble will simply conceal the points it covers.
Colour as a fourth channel is usually one too many. If three variables are genuinely needed, small multiples of a scatter often communicate better than one crowded bubble chart.

How to read the output

Read position first and size second. If the finding depends on the sizes, the chart is the wrong one and a weighted regression is the right one.
Overlapping bubbles hide points behind them. Sort so the largest are drawn first, or reduce the size range.
A bubble chart with a time dimension is usually better as small multiples than as an animation: readers cannot compare frames they cannot see at once.
Size is the least precisely read channel on any chart. Use it for context - which observations are large - rather than for any comparison the argument depends on.

A worked reading

Two countries with GDP of 100 and 400. Encoded correctly, the second bubble has twice the radius and four times the area, and most readers will judge it as roughly two-and-a-half to three times larger - the under-estimation Stevens' law predicts. Encoded by radius instead, the second bubble has four times the radius and SIXTEEN times the area, and readers will report something like eight times. The data never changed; the chart told two different stories, and only one of them was wrong on purpose.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Differences looking enormous	Radius encoding rather than area	Check whether r scales with the square root
No size legend	The scale cannot be recovered	Add three reference circles
Bubbles hidden behind others	Draw order	Sort large to small; add transparency
Zero-valued points invisible	No valid radius	Mark them distinctly and say so
Reader comparing two similar bubbles	Area judgement is unreliable there	Label the values
Four variables encoded	Beyond what one chart carries	Use small multiples

Common mistakes

Scaling by radius instead of area, which exaggerates large values by squaring them. This app scales area.
Using size for the outcome. Nobody can read it accurately enough to support a claim.
Too many bubbles: past a few dozen the chart is an unreadable overlap and a plain scatter is better.
Encoding a fourth variable as colour as well. Position, size and hue in one chart exceeds what most readers will decode, and the fourth variable usually deserves its own panel.

Where to read this properly

Cleveland and McGill (1984), JASA 79(387).
Stevens (1957), "On the Psychophysical Law", Psychological Review 64(3).
Tufte, The Visual Display of Quantitative Information (2001), on the lie factor.

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Bubble 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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