Science Puzzle
The Graph That Starts at Ninety
A survey finds approval rising from 94 to 97 percent over four years. One newspaper plots it with the y-axis running from 90 to 100, producing a steep climb, and headlines it "surge in approval". Another plots the same figures with the axis from 0 to 100, producing a nearly flat line, and calls it "broadly unchanged".
Neither chart contains a false number. Is either one dishonest, and how should you decide which axis is right?
The Answer
Both charts are truthful and neither contains a false number, which is exactly what makes this worth thinking about carefully. The manipulation, where there is one, happens in the framing rather than in the data.
A truncated axis magnifies small changes. Starting at 90 turns a 3-point difference into a line that climbs most of the height of the chart, and the reader's eye reads slope as significance. That is not a neutral choice. But the popular rule "the axis must always start at zero" is wrong too, and applying it blindly produces its own distortion: a chart of body temperature from 0 to 40 degrees would render a lethal fever as an invisible wobble.
The real question is not what the axis rule says, it is what a meaningful change would be. And that is a substantive question about the subject, not about charting. If approval below 95 percent triggers a review and above 96 triggers a rollout, then a 3-point move is enormous and the truncated axis is the honest one. If nothing whatsoever changes until approval halves, the flat line tells the truer story.
So the chart is not merely presenting the data. It is smuggling in an answer to the question "does this amount of change matter?", and it is doing so silently, through a choice most readers will never consciously notice. That is the mechanism to watch for, because it generalises: the same trick works with axis scaling, with the choice of start and end dates, with linear versus logarithmic scales, and with what gets binned together.
The defensive habit is simple and quick. Before reading the shape of any line, read the axis. Ask what it starts at, what it ends at, and what size of change would actually be meaningful in this domain. Then look at the line. Once you do that in that order, the picture stops doing your thinking for you.
The principle: Axis truncation and graphical framing. A truncated axis exaggerates small changes and a zero-based one can hide important ones. The correct scale depends on what size of change is meaningful, which is a question about the subject, not the chart.