LogicalDUAL-USE

Dual-Axis Chart

What it is

Plotting two series against two separately scaled vertical axes on one chart, so that by choosing the scales the designer can make the lines cross, converge, track each other or diverge wherever the argument needs them to.

How it works

Two independent axes give the designer four free choices — the origin and the scale of each — and with four free choices almost any two rising series can be made to march together and almost any two can be made to cross at a chosen date. Viewers read the closeness of two lines as a relationship and their crossing as an event, because that is what those things mean on a single-axis chart. Worked: series A runs from 100 to 110 while series B runs from 1,000 to 2,000; put A on an axis from 95 to 115 and B on one from 900 to 2,100 and the two lines rise in lockstep, apparently linked; put A on an axis from 0 to 200 and B stays as it was, and B now soars past a flat A. Nothing in the data changed. The device has honest uses — temperature and pressure on an instrument chart, price and volume on a stock chart — where the reader knows both scales and no claim about the relationship rides on the picture. The manipulation is to remove or shrink the axes, or to set them so the lines tell a story, and then to describe the story as what the data show. Indexing both series to a common start, or drawing two small panels, removes the freedom.

Real-world examples

  • •At a September 2015 congressional hearing, Representative Jason Chaffetz displayed a chart, sourced to Americans United for Life, in which a line for Planned Parenthood abortions (about 327,000 in 2013) was drawn above a line for cancer screenings (about 936,000) with no vertical axis; the two series had been scaled independently so that the smaller number appeared larger.
  • •Tyler Vigen's Spurious Correlations (2015) used dual-axis charts deliberately — cheese consumption against deaths by bedsheet entanglement — to show how easily two unrelated series can be made to appear to move together.
  • •Overlays of atmospheric carbon dioxide and global temperature have been drawn by climate advocates with axes chosen so that the lines track, and by skeptics with axes chosen so that they diverge; the same two series support either picture, which is why neither picture is evidence.
  • •Corporate earnings decks often plot revenue as bars and margin as a line on a second axis scaled so that a falling margin looks flat, or a flat margin looks rising, depending on the quarter's message.

Ethical guidelines

Where the line is

A second axis is legitimate on an instrument or market chart where both scales are labeled, the reader knows the units and no claim about the relationship between the series depends on the picture; it becomes manipulation when the scales are set so that the lines track, cross or diverge to make a point, when the axes are hidden, or when the resulting picture is described as what the data show.

  • ●If you must use two axes, label both fully, start both at zero or say why not, and state what relationship, if any, you are claiming between the series.
  • ●Prefer indexing both series to a common base date, or two aligned panels, whenever the point is that the series move together; those forms cannot be tuned to manufacture the impression.
  • ●Never remove the axes from a two-series chart; an axis-free dual-series chart is a drawing, not a graph.
  • ●Do not describe lines crossing or converging as an event in the data when the crossing point is a product of the scales.

How to defend against it

  • ►Find both axes and read their ranges; if either is missing, treat the chart as an illustration and go to the numbers.
  • ►Ask what the chart would look like if both series were indexed to 100 at the start, and if possible redraw it that way; relationships that survive are real, relationships that vanish were the scales.
  • ►Treat a crossing point as a claim needing the underlying numbers: at the date the lines cross, what were the two values, and does one really exceed the other in any meaningful unit?
  • ►Ask whether the two series are even measured in comparable units; if not, the picture cannot show a relationship, only a coincidence of shapes.

References

  1. Cairo, A. (2019). How Charts Lie: Getting Smarter about Visual Information. W. W. Norton
    Treatment of dual-axis charts and axis-free overlays, including the 2015 Planned Parenthood hearing chart.
  2. Tufte, E. R. (2001). The Visual Display of Quantitative Information (2nd ed.). Graphics Press
    The principle of graphical integrity: the representation should not be tunable to produce an impression the data do not support.
  3. Vigen, T. (2015). Spurious Correlations. Hachette Books
    Deliberately constructed dual-axis charts showing unrelated series appearing to move together.
  4. Wainer, H. (1984). How to display data badly. The American Statistician, 38(2), 137-147
    The catalogue of scale and axis choices that hide or fabricate relationships in charts.
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