Losing the shared baseline sharply degrades position judgment

What it is

Nonaligned positional comparison occurs when two marks use the same unit, domain, and transform but cannot be projected directly to one reference line. Segments away from the baseline in a stacked bar and spatially separated panels with identical scales require readers to recover a reference before comparing. Classic graphical-perception work ranked position on nonaligned scales below common-scale position. The size of the loss depends on task, layout, and available aids rather than a universal multiplier. This classic condition is not the same as conversion across different scales.

“Shared baseline” here means a common comparison reference, not necessarily numerical zero. Points may share any clearly marked coordinate domain. Bar segments use length as well, bringing stronger requirements for a common start and meaningful zero.

Why it happens

Without a common reference, comparison adds reference identification, working-memory retention, and eye movement. Both endpoints of an upper stacked segment may move, turning the task into length or a difference between positions. Separated panels require readers to correspond ticks across regions even when their mappings are identical. Gridlines, direct labels, linking, or a computed difference can remove some operations, but they do not restore a directly visible common baseline between marks.

This leaf concerns identical mappings whose spatial references are offset. A mismatch in unit, domain, linear or logarithmic transform, direction, projection, or pixel range changes what screen position means and constitutes a different mapping-alignment problem.

Studying it

Hold data and mark size constant while manipulating common axis, separated but identical scale, stacked start, and direct labels. Ask for ratio, difference, order, or target location, and report error distributions, response time, and strategy. Effects from classic common-scale proportion estimation should not be copied into trend or shape tasks. The original experiments and web replication provide baselines, but a new layout should be tested at its deployed size and range.

Eye tracking and interaction logs may reveal cross-panel shuttling and scale lookup, but saccade count is not comprehension cost by itself; combine it with answer accuracy and outcome. Accessibility evaluation should test whether a screen-reader table or structured data navigation aligns values by field. A visually nonaligned chart may become aligned in its data representation, so visual and nonvisual views require separate assessment.

Where it stops holding

When the task concerns within-group pattern, normalized shape, or anomaly rather than absolute cross-group magnitude, independent scales can use pixels more effectively and reveal local structure. Small multiples may therefore use independent ranges for shape comparison, but must prevent panel height from being read as absolute value. A few exact comparisons may be better served by direct numbers, a sorted table, or a computed difference.

Some spatial arrangements cannot be aligned without destroying meaning, including geographic location and network topology. Point-estimate accuracy also cannot replace interval overlap, distribution, or measurement-error reasoning when data are uncertain. Nonvisual readers should not have to infer values from screen coordinates.

Applying it

• Enumerate mark pairs that require cross-group comparison. Give them a shared unit, domain, transform, direction, and pixel range, or switch to a common-reference form such as a dot plot, grouped bar, or sorted table.
• Use only baseline-aligned stacked segments for precise comparison. If upper segments matter, add facets, direct differences, or interactive reordering. Label every independent facet scale rather than omitting ticks that create a false impression of sharing.
• When normalized shape is the task, name the normalization in heading, axes, and accessible description. Across maps, state projection, extent, and scale; similar screen position must not imply comparable distance.
• Validate error and time on the intended comparison and expose a sortable table, numerical summary, and intervals. Reintroduce a common reference or reframe the task when readers repeatedly convert scales or mistake local ranges for a global one.

Related

• Same group: U1.02.1 Position along a common scale is the most accurate channel · U1.02.3 Position carries both quantitative and categorical data and is the scarcest channel · U1.02.4 A 2D plane has only two position channels; once allocated, they are spent · U1.02.5 Position judgment depends on alignment; axis misalignment cancels the advantage
• Adjacent: U1.03.1 Length judgment requires a common starting point · U2.15.5 Small multiples compare shapes, not precise values
• Search terms: position along nonaligned scales · common baseline · stacked comparison