LogicalDUAL-USE

Pictogram Scaling

What it is

Representing quantities with pictures — moneybags, barrels, people — scaled by height, so that doubling the number produces a picture four times the area and, in perspective, eight times the volume, which is what the eye reads.

How it works

A bar encodes a number in one dimension; a picture encodes it in two, or three if drawn with depth. When a designer doubles a moneybag's height to show a doubled sum, the width doubles with it, the area quadruples, and a viewer who sees the picture as an object sees eight times the money. Huff drew the example in 1954; Tufte measured the general case as the lie factor, and his standard example is a 1978 New York Times chart of fuel-economy standards rising from 18 to 27.5 miles per gallon, a 53 percent increase drawn as a road widening from 0.6 to 5.3 inches — a 783 percent increase, a lie factor of 14.8. Cleveland and McGill showed that people judge lengths on a common scale well and areas and volumes poorly, so pictorial scaling both exaggerates and blurs. The same arithmetic governs bubble charts whose bubbles are scaled by radius rather than area, and three-dimensional pie charts whose front slice is drawn largest. The honest tradition is Otto Neurath's Isotype of the 1930s: repeat a standard icon, one per unit, so that ten bags are ten bags. A single icon scaled by area with the scale stated is defensible; a single icon scaled by height, or drawn in perspective, is not.

Real-world examples

  • •Tufte's 1978 New York Times fuel-economy chart: mandated mileage rising 53 percent between 1978 and 1985, drawn as a receding road whose lines grew by 783 percent, the canonical lie factor of 14.8.
  • •Huff's How to Lie with Statistics (1954) shows two moneybags for weekly wages of 30 and 60 dollars; the second is drawn twice as tall and therefore four times as large on the page, and larger still if the reader imagines it as a bag.
  • •Bubble maps and bubble charts in news graphics that scale the circle's radius rather than its area to the value show a country with twice the figure as a circle four times the size, a recurring error even in reputable outlets.
  • •Three-dimensional pie charts in annual reports, in which the slice placed at the front is drawn with a visible edge and foreshortened neighbors, routinely make the featured segment look larger than its share.
  • •Neurath's Isotype charts of the 1930s, and modern infographics that follow them, show quantities as rows of identical icons — one figure per million people — which cannot exaggerate because nothing is scaled.

Ethical guidelines

Where the line is

Pictorial charts are legitimate when a standard icon is repeated per unit, or a single icon is scaled by area with the scale stated, so that the visual ratio matches the numerical one; they become manipulation when an icon is scaled by height or drawn in perspective so that the eye reads a squared or cubed ratio, and the presenter relies on that reading.

  • ●Scale pictures by area, never by height, and say in the caption that area represents the quantity; or better, repeat a standard icon per unit.
  • ●Do not draw quantitative pictures in perspective or with implied volume.
  • ●Compute the lie factor before publishing: the ratio shown on the page divided by the ratio in the data should be close to one.
  • ●Use bars or dots when precision matters; use pictures for engagement only when they pass the same test.

How to defend against it

  • ►Read the printed numbers and ignore the pictures; if there are no printed numbers, there is no chart.
  • ►Compare heights, not areas: measure the two icons' heights with a finger and compare that ratio with the stated ratio; if the stated ratio is two and the picture looks like four or eight, you have found the device.
  • ►For bubble charts, ask whether the values are proportional to the area or to the radius; the difference is the square of the ratio.
  • ►Treat any three-dimensional pie or bar chart as decorative; the depth has no data in it and distorts what does.

References

  1. Tufte, E. R. (2001). The Visual Display of Quantitative Information (2nd ed.). Graphics Press
    The lie factor and the 1978 fuel-economy chart with its lie factor of 14.8.
  2. Huff, D. (1954). How to Lie with Statistics. W. W. Norton
    The moneybag example of one-dimensional scaling producing two- and three-dimensional exaggeration.
  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
    Experimental ranking of graphical encodings: length judged accurately, area and volume poorly.
  4. Neurath, O. (1936). International Picture Language: The First Rules of Isotype. Kegan Paul
    The Isotype convention of repeating standard icons rather than scaling them, the honest alternative.
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