Usually I (and other statisticians who think a lot about graphics) can’t stand this sort of graph that overloads the y-axis:
But this example from Isabel Scott and Nicholas Pound actually isn’t so bad at all! The left axis should have a lower bound at 0—it’s not possible for conception risk to be negative—but, other than that, the graph works well.
What’s usually the problem, then? I think the usual problem with double-y-axis graphs is that attention is drawn to the point at which the lines cross.
Here’s an example. I was searching the blog for double-y-axis graphs but couldn’t easily find any, so I googled and came across this:
Forget the context and the details—I just picked it out to have a quick example. The point is, when the y-axes are different, the lines could cross anywhere—or they don’t need to cross at all. Also you can make the graph look like whatever you want by scaling the axes.
The top graph above works because the message is that conception risk varies during the monthly cycle while political conservatism doesn’t. It’s still a bit of a cheat—the scale for conception risk just covers the data while for conservatism they use the full 1-6 scale—but, overall, they still get their message across.