Computing Lie Factor by Dividing Percentages

In the book “The Visual Display of Quantitative Information”, there is a term “Lie Factor” defined on page 57. An example computation of lie factor is given. Basically, the actual data varies from 18 to 27.5, but graphically it varies from 0.6 to 5.3. So the actual change is 1.53, the graphical one is 8.83, and resulting lie factor is 5.78.
The computation in the book gives a lie factor of 14.8, which is incorrect.

Simpler example: if something changes by a factor of 2, and the graphic shows that it changed by a factor of 4, then the lie factor is 2. However, if we divide percentages, we get 300% / 100% = 3.

Therefore, lie factors reported in “Visual Display…” are exaggerated. If original data changes by a factor of a, and the graphics data changes by a factor of b, then the lie factor is b/a, but ET’s factor is (b-1)/(a-1).

Example: real data shows 1,1.01, graphics shows 1,2.
The lie factor is not 100, but 1.98. One could say “well, but the growth here is 1%, there it’s 100%, so it’s exaggerated by a factor of 100!” But this logic is incorrect. The following example illustrates it:
Suppose the original data is 1,2,3. The graphic shows 1,8,12.
If we scale the effect shown in the graphic down by a factor of 4, we get the correct growth. So the lie factor is 4. But if we divide percentages, the lie factor is either 7 or 5.5, depending on which pair of numbers you use to compute it. If the data went up to 100 and the graphic to 400, the Tufte lie factor would give 4.03 (=399/99). That is, only in the limit would it converge to the right number.

Regards,

Alexei Lebedev