choropleth mapping and standardization

Choropleth maps, like the one above, use the visual variable of value (aka shade or lightness), sometimes in concert with hue or saturation, to present data about featues. Academic cartographers teach that this symbology should only be used in certain circumstances.

  1. The phenomenon being mapped must be thought to vary only between enumeration units, and not within them. That is, the phenomenon is observed to change abruptly at enumeration unit borders (abrupt).
  2. There is little variation in the shape/size of enumeration units (uniformity).
  3. The data itself must be standardized (divided) by another attribute value of the feature, typically land area or a related variable. (standardized).
  4. The phenomenon being mapped is continuous, that is, present everywhere (continuous).

Though I think there’s reason to talk about/problematize all four, I’m most interested in the third criterion: standardization. It is taken as gospel in academic cartography that for a choropleth to “work”, the underlying data must be standardized. The need for standardization, as stated by Dent (1996), is because “the varying size of areas and their mapped values will alter the impression of the distribution.” Slocum (2005) backs up Dent, writing that standardization is necessary to “account for varying sizes of enumeration units”.

These same cartographers, though, stress that standardization need not be by land area. Slocum, for example, lists three methods of standardization other than land area (for example, crimes per capita, or really any per capita variable). Using non-area variables is justified by Slocum because “this approach indirectly standardizes for area because larger areas tend to have larger values for both attributes”.

This seems questionable, especially since small enumeration units with high values are a problem standardization was designed to address. My point: dividing a variable (say, elderly population) by a non-area variable (say, total population) does nothing to address the issue of varying unit size on the resultant choropleth map.

It seems to me we’re left with two options.

    Either,

  • We must standardize our data, and it must be by land area, to correct for the varying size of areas on the map.
  • Or,

  • We can standardize by any other variable, and indeed abandon standardization altogether by mapping raw totals.

I won’t weigh in just yet, as I could really go either way. Are there other justifications for standardization that don’t require standardization by land area?

5 Comments

  1. Often the polygons in a choropleth map aren’t directly representing their land area they’re representing a phenomena occurring within a subset of the area in the polygon. In the case of elderly population it doesn’t matter that a polygon is 100 sq mi. or 10,000 sq mi. it is really just a lasso that defines the bounds of the phenomena. Area is not relevant in many cases.

    Kasey
    Posted May 31, 2008 at 12:13 pm | Permalink
  2. I’d think that in cases where the area of enumeration units is not relevant–or, more more precisely, where the boundaries of the units are unrelated to the phenomenon being mapped–there’s a problem with some of the other “rules” of choropleth mapping, probably the rules about being abrupt and ubiquitous. It seems to happen all the time, actually. A common example would be a population map of the US by county: the boundaries are arbitrary political impositions that are largely irrelevant to population distribution, and just for good measure they do vary rather widely in shape and size. Strictly speaking, some phenomena (such as population), whether standardized or not, are inappropriate for choropleth maps because the most likely enumeration units have little to do with the distribution of the phenomena.

    Anyway, that’s a bit of a tangent, but I suppose I am attempting to make the point that the supposed laws of choropleth mapping are already violated all over the place. In regard to the particular question at hand, I agree that there’s no real reason to insist on standardization by something other than area. As I’ve mentioned to you in outside conversation, Zach, I think that there are arguments to make for standardizing the data by other variables for the purposes of meaningful comparisons, but that these arguments are absent any spatial significance. That is, standardization by variables other than land area, if it is necessary, is not an issue unique to choropleth maps and should not be our (cartographers’) rule. Granted, I can see Slocum’s assertion that “larger areas tend to have larger values for both attributes” being true sometimes, if not often, but there’s obviously no guarantee of that, especially since that’s why we often standardize by land area in the first place, as you said.

    Andy
    Posted May 31, 2008 at 12:14 pm | Permalink
  3. Hang on, I shouldn’t have posted that comment yet; I haven’t chosen a side from the options you presented!

    But (let’s say in typical Andy style) I won’t choose a side, because I think neither should be universal. With respect to standardization, I see two basic situations. 1) The mapped phenomenon (e.g. population, even though I said before it’s not appropriate for choropleth maps at all) is affected by land area and therefore should be standardized by land area; and 2) the phenomenon (e.g. some economic indicators) is not or is only distantly affected by land area, in which case we can standardize by something or not, but it’s not a cartographic decision, as my previous comment argued.

    Andy
    Posted May 31, 2008 at 12:14 pm | Permalink
  4. i find choropleth mapping useful for another reason:

    I am mapping by enumeration units that are IDENTIFIABLE by the map reader.

    The map units are also accountable in that I can trace the data back to the appropriate jurisdiction. Sometimes this is state-based, others county or zip code or nation.

    When a phenomenon is NOT well spread inside the polygon I either try to show the point data or limit the color coding to just the appropriate subareas (see: http://portfolio.kelsocartography.com/albums/portfolio.kelsocartography.com/2008/FarmDay1Map.jpg).

    There is another alternative to show small areas with choropleth but large areas by symbol inside the large polygon: http://portfolio.kelsocartography.com/albums/portfolio.kelsocartography.com/2006-b/vaSenate.jpg
    versus
    http://portfolio.kelsocartography.com/2006-b/meExurbs.jpg.html

    I am more interested in the raw totals.

    Posted May 31, 2008 at 12:17 pm | Permalink
  5. Very interesting discussion…

    What you are referring to as “Standardization” can also be called “Normalization.”

    Kyle
    Posted October 7, 2008 at 11:45 am | Permalink

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