How a Chart Misleads

Bars and lines should usually start at zero. When a chart starts its bottom higher up — say at 90 instead of 0 — a small change fills the whole picture and looks enormous. Two other tricks: stretching a chart tall and thin to make a gentle slope look steep, and showing only the few months that happen to prove a point.

The eye reads a bar's height as its value, so a chart is only honest when height is proportional to the number. A truncated axis — one that does not begin at zero — breaks that proportion: it magnifies small differences into large-looking ones. This is the most common distortion, and the easiest to catch once you check where the axis starts.

Two relatives of the same trick: stretching the scale, where a tall, narrow frame turns a gentle rise into a cliff, and cherry-picking the window, where only the stretch of time that supports a claim is shown while the fuller record is hidden. In every case the data is accurate; the framing does the lying.

Three distortions cover most misleading charts. Truncation: cropping the axis so it starts above zero, which inflates ratios the eye reads off bar heights. Scale stretching: choosing an aspect ratio or a nonlinear scale so a modest slope reads as dramatic. Window selection: displaying only the interval of time that flatters the claim and omitting the rest.

Undoing each is a fixed reflex. For truncation, ask where the axis begins and recompute the real difference. For stretching, mentally re-square the frame or read the axis numbers instead of the shape. For a cherry-picked window, ask what the series looked like before and after the shown slice. A chart's message and its axes are two separate things; always read both.

A picture of numbers should tell the truth. If you cut off the bottom of a bar chart, a tiny change can look huge. The bars lie, even when the numbers are honest. Always look at where the bottom starts.

Tufte formalizes this as the lie factor: the ratio of the size of an effect shown in the graphic to the size of the effect in the data. A truthful chart has a lie factor near 1; truncation and area tricks push it far from 1. The principle of proportional ink — the ink representing a value should be proportional to the value — is the operational rule a zero baseline enforces for bars.

Zero baselines are not universal law. For bar charts encoding magnitude by length, a zero baseline is mandatory; for line charts of an interval-scaled quantity such as temperature, forcing zero can itself mislead by flattening meaningful variation. Logarithmic scales are honest for multiplicative data and dishonest when smuggled in to tame an alarming linear trend. The judgment is always: does the encoding preserve the comparison a reader will make?

Graphical perception research (Cleveland and McGill) ranks the visual channels by accuracy: position along a common scale is decoded most reliably, area and angle far less so. Distortions exploit this hierarchy — pie and bubble charts hide differences in poorly decoded channels, while truncated bars corrupt the position channel we trust most. The lie factor quantifies the resulting bias, but perception, not arithmetic, is what the manipulation targets.

Window selection is the graphical face of the garden of forking paths: choosing the interval after seeing the data is an unacknowledged multiple comparison, and any sufficiently long series contains sub-windows supporting nearly any slope. Even a defensible default encoding embeds rhetorical choices, so integrity is not a property of a single chart but of disclosed provenance — what was shown, what was omitted, and why.