Length encodings crossing the break lose all comparability

What it is

The group's most thorough failure lands on bar charts: a bar whose length straddles the break has its lower half under one conversion and its upper half under another, while the reader judges the whole length as one. This is no longer "reduced precision" but revocation of the encoding — the correspondence between length and value has no definition on a cross-break bar, and comparing the lengths of any two such bars is meaningless. A truncated-end bar at least admits correction by an amplification factor (first leaf); a cross-break bar has no correction formula at all, since two bars can straddle different intervals.

Why it happens

A bar is read as a single continuous length from baseline to tip, and the break cuts that length into the sum of two distances under different scales; the "sum" has no conversion meaning — like "three kilometres plus two pounds." Worse, the failure is undetectable: a cross-break bar looks identical to an ordinary bar (break marks usually sit on the axis and do not cut the bar body — see the next leaf's marker problem), so readers cannot know which bars are "poisoned." One chart then mixes three classes of bars — below the break, above it, and crossing it — the first two still comparable within their sides, the crossing class comparable with neither, yet all three visually homogeneous, and the comparing cannot be policed.

Where it stops holding

The failure is precisely confined to marks crossing the break: bars lying wholly on one side retain that side's uniform scale and remain internally comparable (though cross-class comparison is still forbidden). Points are position encodings — a cross-break point suffers location distortion (the second leaf's distance problem) without compounding it into "length meaning" itself, so points with a broken axis are "wrong but computable," bars with a break "wrong and incomputable." The engineering conclusion is binary: bars present means no break; a break needed means switch to points — there is no third road.

Applying it

• Hard rule: length/area-encoded marks (bars, histograms, areas) and broken axes are mutually exclusive; review rejects outright, no case-by-case exemption.
• Where outliers motivate the break on a bar chart, use the fifth leaf's options (facets, paired charts above and below, clipped outliers with labels — anything but log-axes with bars).
• Verification: build two pairs of cross-break bars (small and large value differences) and ask readers to rank by length; rankings departing from truth demonstrate the failure — good team-training material.

Related

• Same group: U3.02.1 A broken axis removes a value interval from the middle of the scale · U3.02.2 Across the break, equal distances no longer mean equal values · U3.02.3 Break markers are often too small to notice, equal to unmarked · U3.02.5 Facets or log scales usually replace the broken axis
• Nearby: U3.01.1 Length encodings must start at zero · U2.02.2 The baseline must start at zero
• Search terms: broken axis bars · length encoding · crossing break · bar comparability