How wide an interval band looks on screen depends on the y-axis scale, not just the real uncertainty

What it is

A confidence interval's visual width on a chart (the error bar's length, the band's pixel height on screen) is not an intrinsic property of the uncertainty but the joint product of "actual interval width" and "y-axis scale." The same ±0.5 interval occupies 5% of the height on a chart with a 0-10 y-axis (visually narrow) but 25% on a chart with a 0-2 axis (visually wide). Readers' intuition about the size of uncertainty is built on visual width—when two charts sit side by side, the difference in visual width may come entirely from the y-axis scales rather than any real difference in uncertainty. This is the most commonly overlooked trap when placing interval charts side by side (small multiples, comparison panels).

Why it happens

Visual width = actual width × pixels-per-unit ratio. The second factor is set jointly by the y-axis range and the plot area's height, both of which are usually configured per chart (auto-scaling fills the plot area with the data). Auto-scaling's intent is to maximize each chart's signal, but its side effect is that the visual expression of uncertainty is also distorted by each chart's own scaling: a low-variance series, magnified, shows a visually wide band (many pixels); a high-variance series, compressed, shows a visually narrow band (few pixels)—possibly the reverse of reality. The visual system does not automatically normalize for scale—it compares pixel widths directly, which is especially dangerous in small-multiples layouts because the side-by-side arrangement implies "these charts are directly comparable." Unlike position judgments (most accurate on a shared scale), width judgments have no natural cross-chart reference; each chart's own axis is the only reference frame.

Where it stops holding

The cross-chart width trap only appears when y-axis scales differ: with multiple charts sharing one y-axis range (shared axis), visual widths are directly comparable. The design fix in comparison contexts is to force a shared axis—but that can flatten low-variance series against the bottom, obscuring their own patterns, re-creating the tradeoff between "comparable" and "individually readable." Cross-chart width comparison has another confound: if the two charts use different units (percentage vs absolute count), the actual widths are incomparable regardless of visual width. For same-unit charts, a shared axis plus labeled numeric ranges is the minimum for making widths comparable.

Applying it

• When uncertainty must be compared across charts, force a shared y-axis range and label each chart's axis range in the corner for verification.
• When a shared axis is impossible, annotate each chart's interval numerically (e.g., "±0.5") so readers compare numbers rather than pixels.
• Default comparison panels (small multiples) to a shared y-axis; if a flattened series becomes unreadable, draw it separately rather than rescaling the axis.
• Verification: place two charts with intervals side by side and ask which has greater uncertainty; if the reader's judgment disagrees with the ordering of actual numeric widths, check whether the two y-axis ranges differ.

Related

• Same group: U8.02.1 Whether an error bar shows standard deviation, standard error, or confidence interval must be stated · U8.02.2 Overlapping intervals between two groups do not imply a non-significant difference · U8.02.3 Interval width varies with sample size; sample size must accompany it · U8.02.4 Gradient bands create less certainty illusion than hard-edged intervals
• Nearby: U4.03.1 Truncating the y-axis exaggerates differences · U8.01.2 Error bars and interval bands are the basic tools
• Search terms: axis scaling · shared axis · cross-chart comparison