Classification for Choropleth Maps

Objectives

  1. Talk about Classification
  2. Do Classification: Event 07


The set of classification methods is large (Dent p. 145), but there are a few to remember:

Then a lot of ones that you might need to use once in a while

  • Arithmetic progression: constant increase (decrease) in "width" of class
  • Geometric progression: constant multiplier used to derive width of class
  • Jenk's Iterative ("optimal") minimize within class standard deviations (variance) [ESRI calls this "natural breaks"]
    (see Dent 147-149 on use of F-ratio and weighting)
  • Arbitrary breaks: given externally (laws, regulations, natural process)
  • Standard deviations: statistical distribution
  • Nested Means works by successive halving at the mean (2,4,8,16, ...)

    • Objectives of class interval selection

    (after Jenks and Coulson 1963)


    Encompass full range of the data
    No overlapping values
    No vacant classes
    Enough classes to retain "accuracy" (Resolution?); or too many to inflate accuracy
    Divide into reasonably equal groups / logical mathematical relationship


    These criteria cannot be satisfied simultaneously!
    What kind of equality: along number line of attribute value? number of objects? area?
    Outliers create gaps; graphic symbols (grey shades) have limitations; arbitrary spatial units

    Special Concerns:

    Not all attributes are uni-directional. Not all class breaks are really under your control.

    Bi-polar data: Zero in the middle; two scales (two hues?)
    Fixed external breaks from regulation, physical limits, etc.
    (freezing point of water? carrying capacity...)

    Reminder about Raw Values:

    Choropleth maps have imposed an abitrary set of objects on the landscape, so the distribution of the variable has been gathered into unequally sized units.
    [This is often called the "Modifiable Areal Unit Problem" (MAUP) in statistical geography.]
    Consequently, a raw value (like a count or a total for a unit) records partially how big the spatial unit is, not just how concentrated the phenomenon is at that place.
    Conversion to a rate (of some kind) [or cartographers will call it a derived value] provides a way to standardize to remove the effect of different sized spatial units.
    Examples:

     Raw value:   Derived value:
     Population

      population density (persons/area)

    distance to nearest person (square root(area)/persons)

     Tax revenue in $   $ of tax revenue / person
     Number of persons who can read  Percent of adult population who are literate


    Version of 11 April 2003