The Lie Factor

No, not a post about the new series of a popular show aimed at getting us to purchase manufactured "pseudo-talent" - but a real "measure" of how distorted a graph can be.

Take this:
Leaving aside the obvious comments on gridlines, data labels and 3D effects - the chart is widely misleading.

The 2011 to 2012 results show an increase of 16% (from 49 to 65%) but the data jump covers approximately 50% of the visible chart - thus massively over emphasising the 16%.

Professor Edward Tufte (bio here) defines the "lie factor" as:

where the "effect size" is:

From the data- the size of the effect = (65-49)/49 = 0.327
From the chart (in cms) - the size of the effect (3.7-1.3)/1.3 = 1.846

Lie factor = 1.846 / 0.3265 = 5.65

Tufte: To ensure the integrity of a graphic, its Lie Factor should have a value between 0.95 and 1.05. If the value is less or greater, it indicates a substantial (and often intended) distortion, far beyond minor inaccuracies (e.g. caused by plotting). (ref)

With some Excel-fu:

The chart still shows the 16% rise from 2011 to 2012 - but it's not distorted / magnified as before.

From the chart - the size of the effect (measured with a ruler): (5-3.8)/3.8 = 0.316. So the lie factor in this chart is 0.316 / 0.327 = 0.97 (and only not 1.00 because I can't measure in fractions of a cm more accurately with the plastic ruler I have to hand).

Call to action

  1. Schools - please don't purposefully distort the truth to imply a greater impact than the data shows
  2. Consider the "lie factor"
  3. No gridlines
  4. No 3D
  5. Use data labels correctly

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