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

From: Jim Lemon <jim_at_bitwrit.com.au>
Date: Wed, 26 Mar 2008 20:51:22 +1100

>
> 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

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