“False parallelism”—feel free to come up with a better term here—is when a graph has repeating elements that do not correspond to repeating structure in the underlying topic being graphed.
An example appears in the above graphs from Dan Kahan. The content of the graphs is fine (and, more generally, I think he’s making an important point that we all should be understanding more). But I have a problem with the display, which is that the graphs on the left and the right are displaying different sorts of things but are being shown in parallel ways. The graphs on the left show percentages that are constrained to add to 100%; they’re numbers that could (for example) be displayed in pie charts. Mathematically, each of the left graphs is a histogram of a (simple) probability distribution, which one might call p(x). But the graphs on the right show proportions of a different variable, as a function of x. They are graphs of E(y|x). I always find such juxtapositions confusing. The graphs look the same—they even have the same scales on their axes—but they’re showing different things. Some cues are provided by the axis labels, and indeed I ultimately did figure out what they were saying—but it took time, and the effort required to decode the graphs took me away from the big picture.
How would I do it? I’m not sure. I’d probably start with something simple: Just ditch the graphs on the left entirely, and then on the graphs on the right, make the width of the bars proportional to the percentage of people who gave each response. Also I think I’d extend the bars up to 100% so they are gray on the bottom and white on the top; this would emphasize that each of these is a proportion out of 100%.
I’m not saying this suggestion of mine is perfect. My real point is that the structure of a graph sends Gricean messages. We should be aware of these messages and use them to our advantage, not let them use us.
Hey, that was fun! I haven’t done a pure graphics post in awhile.