LogicalDUAL-USE

Truncated Axis

What it is

Starting a bar chart's value axis above zero, or stretching or compressing a line chart's range, so that the visual size of a difference no longer matches its numerical size.

How it works

Bars encode quantity by length, and viewers judge bars by comparing lengths — the most accurate of all graphical perceptions, as Cleveland and McGill showed in 1984, which is precisely why it is worth corrupting. Move the baseline from zero to just under the smallest value and the ratio of the bars becomes whatever the designer wants. Tufte named the measure: the lie factor, the size of the effect shown in the graphic divided by the size of the effect in the data; an honest chart scores near one. The worked case is the 2012 Fox News chart of the top US income-tax rate: 35 percent now against 39.6 percent if the Bush-era cuts expired, on an axis starting at 34, so the second bar stood 5.6 times taller for a 13 percent difference. The reverse move, an axis so wide the data flatten, hides a real change. Line charts are less rigid, since temperature anomalies, stock prices and dashboards legitimately zoom into a range; the deception is in bars, in the absence of tick labels, and in pairing a zoomed axis with a rhetorical claim about size. Pandey and colleagues confirmed experimentally in 2015 that truncated axes shift what viewers believe the numbers say.

Real-world examples

  • •In August 2012 Fox News aired a bar chart comparing the 35 percent top income-tax rate with the 39.6 percent that would apply if the Bush tax cuts expired; with the axis starting at 34 percent, the bars suggested a rate more than five times higher. In March 2014 the same channel showed Affordable Care Act enrollment of 6 million against a 7.07 million target with the smaller bar drawn at roughly half the height of the larger.
  • •Bar charts on UK Liberal Democrat election leaflets, showing the party narrowly behind or ahead with bars whose heights bore little relation to the printed vote shares, became a running joke across election cycles from the 2000s onward, satirized by opponents of every party.
  • •In December 2015 National Review tweeted “the only climate change chart you need to see”: global average temperature plotted on an axis from minus 10 to 110 degrees Fahrenheit, which rendered a century of warming as a flat line — the mirror image of the truncated axis, an axis expanded to hide change.
  • •Consumer-electronics keynotes routinely show performance bars (“up to 2x faster”) with no axis at all; the bar lengths are chosen for the slide, not measured from a scale.

Ethical guidelines

Where the line is

A non-zero axis is legitimate on a monitoring dashboard, a stock chart or an anomaly plot where the reader knows the range, the ticks are labeled and no claim about magnitude is attached; it becomes manipulation in an advertisement, a campaign graphic or a slide where the bar lengths are what the audience is meant to take away and the axis was set to produce that impression.

  • ●Bar charts start at zero. If the interesting variation is small relative to the total, use a dot plot or a line chart, or plot the differences directly, and say so.
  • ●Whenever the axis does not start at zero, label the ticks legibly and state the range in the caption; a zoomed axis is acceptable, a hidden one is not.
  • ●Match the words to the picture: do not attach “skyrocketing” or “collapsing” to a chart whose axis was chosen to produce that impression.
  • ●Apply the lie-factor test before publishing: is the change on the page roughly the change in the data?

How to defend against it

  • ►Find the axis origin before reading the bars. If there is no labeled axis, treat the bar lengths as decoration and read the printed numbers only.
  • ►Compute the real ratio yourself: divide the larger number by the smaller. If the bars suggest something very different, the chart, not the data, is the message.
  • ►For line charts, ask what the full plausible range of the variable is and whether the plotted range is a zoom (fine, if labeled) or a compression chosen to flatten change.
  • ►Redraw it. Sketch the bars from zero on a napkin; the manipulation is usually obvious in ten seconds.
  • ►Name the device out loud in a meeting — “this axis starts at 34” — which shifts the discussion from the impression to the numbers.

References

  1. Tufte, E. R. (2001). The Visual Display of Quantitative Information (2nd ed.). Graphics Press
    The lie factor and the principle that the representation of numbers should be directly proportional to the quantities represented.
  2. Pandey, A. V., Rall, K., Satterthwaite, M. L., Nov, O., & Bertini, E. (2015). How deceptive are deceptive visualizations? An empirical analysis of common distortion techniques. Proceedings of the 33rd ACM Conference on Human Factors in Computing Systems (CHI 2015), 1469-1478
    Experimental evidence that truncated axes and related distortions change what viewers take the data to say.
  3. Cleveland, W. S., & McGill, R. (1984). Graphical perception: Theory, experimentation, and application to the development of graphical methods. Journal of the American Statistical Association, 79(387), 531-554
    Position and length along a common scale are the most accurately perceived graphical encodings, which is why corrupting the baseline is effective.
  4. Huff, D. (1954). How to Lie with Statistics. W. W. Norton
    The “gee-whiz graph” chapter: the original popular description of axis truncation as a persuasion device.
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