Length can only encode non-negative quantities; negatives need position

What it is

Signed-value encoding with position and magnitude separates which side of a reference a value occupies from how far it lies from that reference. Geometric length and area are non-negative and cannot express sign alone. In a bar extending left/right or up/down from zero, sign comes from direction and position while length can still encode absolute magnitude. “Negatives need position” therefore requires a directed reference for sign; it does not discard every length cue.

Why it happens

A signed value contains sign and magnitude. A common zero maps one side to positive and the other to negative, with distance from zero carrying magnitude. A dot plot relies mainly on position; a diverging bar combines direction and position with length. A circle area or undirected segment needs an added sign, shape, region, or text label. Color can reinforce sign, but color vision, learned semantics, and output conditions make it unsuitable as the only sign cue.

Studying it

Use the same positive, negative, zero, and near-zero values in diverging dots or bars, magnitude-plus-sign, magnitude-plus-color, and separated panels. Test sign identification, absolute-magnitude ordering, across-zero differences, and exact lookup separately; record sign reversals and missed small values. Manipulate imbalance in positive and negative counts, mark size, labels, zoom, and practice, and include grayscale, color-vision simulation, keyboard, and screen-reader tasks.

Where it stops holding

Absolute values, distances, counts, and durations are non-negative magnitudes and have no sign problem when encoded by length. Separate positive and negative panels can reduce overlap but weaken across-sign comparison, so they need a shared scale and explicit zero. An ordinary log scale cannot include zero or negatives; transformations such as symmetric log change the meaning of distance and must be explained for the analytical task.

Applying it

• For direct signed-value comparison, use dots or diverging bars on a common scale with a visible zero, units, and stated positive direction.
• If length or area carries absolute magnitude, encode sign with explicit +/−, shape, or separate regions. Use color only redundantly and test the legend's semantics.
• Keep near-zero marks selectable at the minimum size. Interaction should expose original value, sign, and reference without silently changing magnitude.
• For screen readers, provide signed values, units, reference, and an ordering or trend summary rather than announcing only color or geometric size.

Related

• Same group: U1.03.1 Length judgment requires a common starting point · 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 · U1.03.5 Arc lengths are harder to compare than straight lengths
• Adjacent: U4.03.1 Diverging palettes suit data with a meaningful midpoint · U2.02.2 The baseline must start at zero
• Search terms: signed values · diverging position · sign and magnitude