[R] Thinking about using two y-scales on your plot?

[Jim Lemon]

hadley wickham wrote:
> Please read this first:
> http://www.perceptualedge.com/articles/visual_business_intelligence/dual-scaled_axes.pdf
> 
> It's a reasoned discussion of why it's a bad idea and proposes some
> alternative methods.
> 
> Another good article is:
> K. W. Haemer. Double scales are dangerous. The American Statistician,
> 2(3):24–24, 1948.
> 
> People have been advising dual-axis plots for (at least) 60 years!
> 
As I am an obvious offender in the dual-ordinate plot field (I actually 
used one once about 25 years ago), I suppose I should at least 
contribute to the debate. Few's paper makes some very good points in my 
opinion. The dual ordinate barplot is too often misinterpreted for 
exactly the reason Few states. Bars starting from zero are just too easy 
to interpret as relative magnitudes. The inquiring reader will find that 
twoord.plot doesn't have a barplot option (although the enterprising 
user can easily hack barplot).

As the paper goes on, Few relies more on assertions than demonstrations. 
Consider the last injunction:

It is inappropriate to use more than one quantitative scale on a single 
axis, because, to some degree, this encourages people to compare 
magnitudes of values between then, but this is meaningless.

The crucial phrase, buried in the middle of this, is "to some degree". 
If the degree to which the viewer realizes that it is meaningless is 
greater than the degree to which that viewer is encouraged to compare 
magnitudes, there does not seem to be much of a problem. No evidence to 
support Few's implied outcome is adduced.

My own use of a dual-ordinate plot arose from a circumstance much like 
the final illustration in the paper. I wanted to show that the 
performance of rats on one aspect of a task was near perfect, while 
performance on another aspect was at chance level. However, instead of 
trying to convert the units into probabilities, I simply used the raw 
units scaled to equate the probabilities and added a horizontal line at 
the level of chance performance. No one complained. Did I successfully 
illustrate the dissociation of performance or merely get away with it? 
Unfortunately, I cannot answer that question, but I would love to have 
someone do a good study to either cheer me or knock me on the head. 
That's the way we improve our illustrative techniques.

Jim