Using graduated point symbols to symbolize a range of quantitative values is not as straight forward as one might think. I offer two reasons.

First, point symbols cover areas of page or screen space while the underlying data are usually referenced to a linear scale (Tufte, 1983, commented on this when he introduced his “lie factor”). Such a mismatch does, indeed, require a PI-based conversion so that symbol areas will increase linearly with data (and not so that symbol radii or diameters increase linearly with data).

Second, but more complicated, cognitive psychologists have found that humans tend to systematically underestimate the sizes of point symbols when they read them. That finding lead Flannery (1971) to develop a method for adjusting point symbol sizes to compensate for this observed human tendancy. Today, we call it the Flannery Compensation Method.

All that said, the graphic at hand is too darn big to allow readers to make any effective comparisons. Chart junk – plain and simple.

References cited
Flannery JJ (1971) “The relative effectiveness of some common graduated point symbols in the presentation of quantitative data”. The Canadian Geographer 8(2): 96-109.

Tufte ER (1983) “The Visual Display of Quantitative Information” Graphics Press; Cheshire, CN.

A visualization like this one goes beyond that. Imagine an article written in two languages, alternating between them randomly. Those who know both languages, or how the writer thinks, would be able to interpret it just fine. But the rest of us would be left scratching our heads, at best. At worst, we might understand parts of it and *think* we understand other parts. It might seem just close enough to what we know that we think we get the point, but we’re actually reading the wrong things into the text.

The purpose of both writing and data visualization is to convey information. If we don’t do so in a way that conveys the information we intend, it’s a failure. And personally, as author of not only a blog, but a book as well, I would most definitely want someone to call me out if I wrote something in a way that would cause this much confusion.

@JR – Typos are one thing, and the fundamentals of data and infographics are another. Typos are simple mistakes that can be fixed easily while the above graphic did a poor job of representing the data and shows an incorrect interpretation. If this were a piece of art, then fine I wouldn’t have been so critical, but this is an infographic that thousands of people saw and in turn, thousands probably made incorrect conclusions. That’s a fact.

Like Jess said, this is the Internet, and we’re all entitled to our opinions. Just like you are – who happened to post a comment here.