A good question deserves good data
When the editor went away...

Rank confusion

This chart, found in Princeton Alumni Weekly, only partially scanned here, supposedly gave reasons for "Princeton's top-rated [Ph.D.] programs" "to celebrate". My alma mater has outstanding academic departments, but it would be difficult to know from this chart!


Due to the color scheme, the numbers that jump out at you are the ones in the bright orange background, which refers to how many other departments are ranked equal to Princeton's in those subjects. It takes some effort to realize that the more zeroes there are in the top buckets (fading orange), the better.

The editor started with a nice idea, which is to convert raw rankings into clusters of rankings. She recognized that in this type of rankings (see a related post on my book blog here), it is meaningless to gloat about #1 versus #2 because they are probably statistically the same. For instance, in the ranking of Architecture departments (ARC), 37 schools (including Princeton) all belonged to the same cluster as Princeton, judged to be a statistical tie.

One of the main reasons why this chart looks so confusing is its failing the self-sufficiency test. It really is a disguised data table, with some colorful background and shadows; the graphical elements add nothing to the data at all. If one covered up all the data, there is nothing left to see!

In the following rework, I emphasize the cluster structure. Each subject has three possible clusters, schools ranked above, equal to, and below Princeton. Instead of plotting raw numbers, the chart shows proportions of schools in each category. The order is roughly such that the departments with the relatively higher standing float to the top. Because a bar chart is used, the department names could be spelt out in their entirety and placed horizontally.


If one has access to the raw data, it would be even better to reveal the entire cluster structure. It is quite possible that the clusters above and below Princeton can be further subdivided into more clusters. This will allow readers to understand better what the cluster ranks mean.



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Rick Wicklin

The editors could have used a data table with a different set of three numbers: the highest ranking for Princeton that is supported by the data, lowest possible ranking, and number of schools in each category. A graphical version of this information would also be useful (it would look something like this: http://bit.ly/ihq41C). Still, I give kudos to the editors for even TRYING to incorporate uncertainty!

One addition I'd make to your graphic would be to indicate the number of programs in each discipline. It seems like this is relevant information, since being at the top in physics (160 programs) is more impressive to me than being at the top in CLA (30 programs). I'd also use the orange shade for Princeton (a school color!), and a different shade for those school ranked above Princeton.

Sarah "Pick A Girl" Smith

I like the cluster structure. It seems to be very easy to interpret.


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