Length judgment requires a common starting point

What it is

Common-baseline length comparison makes several marks extend from one visible origin, so differences between endpoints correspond to differences in length. For charts whose bar height or width represents an absolute magnitude, this shared start is normally the basis of direct comparison. The title does not mean that people cannot compare isolated line segments: without a common origin, the task becomes estimating each segment separately and usually loses the precision contributed by aligned endpoints.

Why it happens

A shared origin supplies both a reference and an aligned set of endpoints, allowing positional difference to support bar-length comparison. With displaced starts, viewers must track both ends of each segment or mentally align the segments. That adds comparison work, but there is no general law that error grows linearly with the offset. Baselines, scales, and gridlines help only when they are visible, consistent, and not interrupted by decoration.

Studying it

Use the same values in common-origin, displaced-origin, and separately scaled conditions, randomizing value pairs and presentation order. Separate ordering, larger-value choice, ratio estimation, and exact-value lookup tasks; record response error, time, and confidence for each. Mark size, stroke width, spacing, labels, device, and viewing distance should be controlled or manipulated explicitly. A relative difference observed for one stimulus set and task is not a fixed perceptual error constant.

Where it stops holding

Floating or interval bars support comparison of starts, ends, or interval widths and need not begin at a global zero. They must not masquerade as absolute amounts accumulated from zero. A dot plot encodes position on a common scale and may reasonably truncate its range; when a bar's geometric length carries the value, a truncated origin changes the visual ratio. Numeric labels add exact values but do not repair misleading geometry.

Applying it

• For absolute amounts accumulated from zero, extend bars from one zero baseline. Reserve floating lengths for intervals or differences, and expose both endpoints.
• Keep important differences discriminable at the smallest display size, high zoom, and dense rendering. Do not let labels obscure the baseline or endpoints.
• Interaction may reveal exact values, differences, or temporary alignment guides, but the core comparison cannot depend only on hover, dragging, or training.
• Give screen-reader users the same category, value, unit, and comparison relation. Test ordering and ratio tasks in both the graphic and its nonvisual representation.

Related

• Same group: U1.03.2 Angle judgments are markedly less accurate than length under equal conditions · U1.03.3 Angles near horizontal or vertical are judged more accurately than oblique ones · U1.03.4 Length can only encode non-negative quantities; negatives need position · U1.03.5 Arc lengths are harder to compare than straight lengths
• Adjacent: U1.02.2 Losing the shared baseline sharply degrades position judgment · U3.01.1 Length encodings must start at zero
• Search terms: common baseline · aligned length judgment · graphical perception