Avoid perfect-square targets when readers must compare rectangle areas

Do not force compared rectangles to perfect squares when readers must judge area. For example, in treemaps and other rectangular area displays, allow slight deviations from 1:1 such as near-square rectangles instead of optimizing every compared rectangle to exact 1:1.

Readers appear to use side lengths as cues when judging area, and that shortcut becomes least informative when both shapes are squares. Slight aspect-ratio differences give the eye more usable evidence for the area comparison.

Mechanism: When compared rectangles are both perfect squares, side-length comparison is a weaker proxy for area, which raises estimation error.

Evidence: In the rectangular area experiment, comparisons involving 1:1 aspect ratios produced the worst performance across both isolated rectangles and treemap displays. The paper interprets this result as evidence that viewers use one-dimensional length comparisons to help estimate area. (Heer & Bostock, 2010)

Notes: The paper found no significant accuracy difference between isolated rectangle displays and treemap displays for this task.

• User Goal: Compare one rectangle’s area against another accurately.
• Task: Exact or near-exact area judgment.
• Data: Quantitative values encoded as rectangular areas.
• Chart Setting: Treemap or other rectangular area display with near-square aspect ratios.
• Audience: Web viewers using standard displays.
• Success Criterion: Lower area-estimation error.

Break it when: Achieving the design would require extreme aspect ratios outside the tested near-square range. Why: The study tested moderate aspect ratios around square, and the paper explicitly notes that extreme aspect-ratio variation is expected to hamper area judgments.

Sacrifice: You give up the strict goal of making every rectangle as square as possible. Risk: Blindly pushing away from 1:1 can create skinny rectangles that are also hard to compare. Mitigation: Allow only moderate deviations from square, not extreme ones.

Mistake: Optimizing compared rectangles toward exact 1:1 when accurate area comparison is important. Why it fails: The study found square-vs-square comparisons to be the least accurate case.

Failure Sign: The rectangles being compared are both perfect squares. Quick Check: Inspect the target rectangles; if the important comparison is square against square, expect higher error. Stronger Test: Compare reader estimates on a 1:1 version against a version where the same rectangles are slightly non-square.

• Relax layout rules that force compared rectangles to exact 1:1.
• Allow moderate near-square aspect ratios instead of perfect squares for the compared rectangles.
• Avoid compensating by creating extreme skinny rectangles elsewhere.