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I find myself more and more struggling over defining break points when displaying choropleth (aka thematic) maps to view by others. Does anyone have any suggested references that help guide, both how to choose the type of scale used and the appropriate number of break points? In particular for the number of bins I have only ever seen arguments for a limiting number (e.g. you should not use any more than 5).


To be more specific about what I am looking for, most references I have come across about the subject are similar to the document referenced by julien in this post, and I'm just looking for a more in-depth discussion about the topic.

A few specific use cases I come across frequently (for examples of my struggles);

  • When displaying data that has a large right skew, I'm typically hesitant to display an exponential scale. I fear (for the audiences I am typically displaying maps to) this would cause a greater amount of cognitive burden reading the scale and mapping actual attribute values to the colors. Are my fears incorrect? Also for these types of distributions I find it difficult to justify any particular number of bins.
  • When displaying many small multiple maps, how do I choose an appropriate scale that allows one to visualize relationships effectively both within and between the small multiples? My de-facto standard when the attribute scales vary to a great extent is to use quintiles within each seperate distribution. Are quintiles too many classifications and creating too great a cognitive burden to compare between the panels? I assume people understand quantile classifications are equivalent to rankings (and thus when classed that way aids in interpreting between panels), is this assumption correct?

I initially wrote a paragraph trying to describe the goals of such maps, but I suspect my goals are pretty typical so it was unneeded. The only thing to clarify again is that these are for viewing by other people (like in reports, publications) and are not really for my own exploratory data analysis (although I would suspect good advice should translate to either). Perhaps a good reference may describe the potential goals of such maps, and trade-offs associated with using different classification schemes. I would be interested in both specific and general references.

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While not an answer, this is more of a concept. I just read an article refering to the "5 second rule" for presentations, but it should apply to maps as well. "...put a [map] on a screen, remove it after five seconds, and then ask the viewer to describe the [map]. A dense [map] fails the test— and fails to provide the basic function of any visual: to aid the presentation." forbes.com/sites/jerryweissman/2011/10/26/… –  RyanDalton Oct 27 '11 at 17:06
    
@RyanDalton, the thought is definitely pertinent to the discussion, and I suspect the 5 second test is not all that different than how people conduct experiments on how statistical graphics are interpreted. I'm hoping I don't have to start conducting experiments though to figure out how to make my classification schemes! Note I'm not sure how well I can conduct a 5 second test on myself after I am already quite familiar with the data I am displaying. –  Andy W Oct 27 '11 at 18:16
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@Ryan The "5 second rule" helps explain why so many presentations seem so dumb and insipid. It's basically saying, "don't dare show anything that is sufficiently rich and interesting that it might actually get the audience's attention and engage them." Indeed, every one of the examples in the Beautiful Maps thread would "fail" this test. Assuming the map is well constructed and explained, perhaps failing this test is a good thing! –  whuber Dec 23 '11 at 20:02
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2 Answers

up vote 5 down vote accepted

A great reference, not cited enough, is "How Maps Works" by Alan M. McEachren (The Guilford Press, 1995/2004). It's not a quick guide but a comprehensive reflexion on how maps are seen and understood, based on a really impressive scientific survey and the knowledge of practitionners.

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Works out well as I just started reading it last night! I recently came across this paper (Harrower and Brewer, 2003) for the ColorBrewer online app that suggests the McEachren book to choose the number of classifications. Besides that I have found Monmonier in How to lie with maps has a discussion of illogical number/color schemes. Not as detailed an argument as I was seeking there but more detailed than anything else I had found so far. I will skim the relevant sections in McEachren to see if it satisfies my curiosity. –  Andy W Jan 3 '12 at 17:06
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You can also look into "Thematic Cartography and Visualization" by T. A. Slocum (Prentice Hall, 1999). It's a bit older but he was a student of G.F. Jenks and i found the book very accessible and directly useful. It has a whole chapter on classifications and an illustration of McEachren map complexity indices. –  Laurent Jégou Jan 3 '12 at 17:23
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I recently purchased Thematic Cartography and Visualization (Slocum et al., 2005), and just skimming it appears to be more than sufficient for my request for general references on the topic of choosing bins. It will certainly give me plenty to read for quite some time, and it wasn't too arduous a decision to buy (there are many older cheap copies floating around).

Note I do not think I would recommend MacEachren's How Maps Work for this question in particular. The book is so monolithic I might have certainly forgot, but I do not remember any straightforward discussion about choosing the number of bins (at least not as straightforward as the chapter devoted to it in the Slocum textbook). If anything I think I remember him mentioning the topic is a bit over-done and has not come to any real conclusion, but I would certainly recommend it as a general reference for data visualization anyway.

There is a crazy amount of literature on the topic, and I will have to do some more self-study to see if I can come up with a more satisfactory answer for classifying the skewed distribution. And I will post back if I have anything more substantive to say.

But for the second question about visualizing small multiple maps I recently came across an article by Cynthia Brewer and Linda Pickle, Evaluation of Methods for Classifying Epidemiological Data on Choropleth Maps in Series (PDF here), that is exactly aimed at my question.

In short there experiments suggest quantiles are the most useful way to represent a series of small multiple maps, both for the ease in interpretation (as I suggested in the question) and the fact that they produce equal area maps in terms of fill when the polygons are roughly the same size. This perhaps is not obvious until you see a counter example, below I have pasted a picture of some small multiple maps in which the classifications are constrained to be equal across the series of different rates of cancer (on page 674 of the cited article).

enter image description here

Because the incidence of liver disease is so much lower than COPD, all of the counties in the top maps tend to fall into the lower classifications. If you can't discriminate patterns within one of the maps you will be unlikely to distingish patterns between maps! Of course if reasonable one should make the classifications consistent, but that is only reasonable for some comparison maps. Also as far as the number of bins they chose 7 in their experiments.

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