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Chapter 7 – The Choropleth Map. Data Classification. Appropriateness of Data. Enumeration mapping – describes areal classified or aggregated data Appropriateness of Data – political boundary (Census Bureau units) Not appropriate – continuous phenomena should not be mapped by choropleth maps

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appropriateness of data
Appropriateness of Data
  • Enumeration mapping – describes areal classified or aggregated data
  • Appropriateness of Data – political boundary (Census Bureau units)
  • Not appropriate – continuous phenomena should not be mapped by choropleth maps
  • Two enumeration data: totals or derived.
  • Sometimes, totals are not suitable for mapping (Fig 7.4)
  • Major Assumption – the value in the enumeration unit is spread uniformly throughout the unit.
  • If data cannot be dealt with as ratios or proportions, then should not be portrayed by the choropleth tecnique.
common methods of data classification
Common Methods of Data Classification
  • No more than 5 to 7 classes
  • Six common methods - equal intervals, standard deviation, Arithmetic progression, Geometric progression, Quantile, Natural breaks, and optimal.
equal intervals
Equal Intervals
  • Useful when histogram of data array has a rectangular shape (rare in geographic phenomena)
  • Advantages: 1) easy to compute the intervals 2) easy to interpret the resulting intervals 3) no gap in the legend display 4) only lowest limits can be shown in legend
  • Disadvantage: skewed data is not appropriate.
calculating steps
Calculating Steps
  • 1. Calculate the range of the data (R)

: R = H – L

  • 2. Obtain the common difference (CD)

: CD = R/(# of Classes)

  • 3. Obtain the class limits by calculating
    • L + 1 x CD = first class limit
    • L + 2 x CD = second class limit
    • L + (n-1) x CD = last class limit
quantile
Quantile
  • Ordered data are placed in classes.
  • Ties can complicate the quantiles method.
  • Advantages - 1) class limits can be computed manually.2) if enumeration units are same, each class will have the same map area. 3) quantile are useful for ordinal-level data, no numeric information would be necessary to create the classification.
  • Disadvantage - 1) gap result may vary. 2) fails to consider data distribution.
  • K = # of enumeration units / number of classes
standard deviation
Standard Deviation
  • Used only when the data array approximates a normal distribution.
  • Advantages: 1) Distribution of data is taken into account. 2) if normal distributed data is used, the mean is a good divider. 3) no gap in the legend.
  • Disadvantage: 1) only work with normal-distributed data. 2) negative values may be in the range
geometric progression
Geometric Progression
  • Useful technique when frequency of data declines continuously with increasing magnitude
  • a, ar1, ar2, ...arn
  • 1) compute common multiplier (a is the lowest value, r is the common multiplier and n is the number of classes
  • use “Xmin x rn = Xmax” to obtain r
  • eg. 118 x r5 = 790 ( use Area as variable) r = 1.46
  • So the interval goes from
  • 118, 118x1.46, 118x1.462, 118x1.463,118x1.464
  • 118-172, 173-252, 253-367, 368-536, 537-790
graphic array
Graphic Array
  • Figure 7.11
  • Class boundaries are identified at places where slopes change remarkably
  • Disadvantage: not suitable for large amount of data
jenks optimization
Jenks Optimization
  • Forming groups that are internally homogenous while assuring heterogeneity among classes
  • groups are created based on gaps.
  • Minimize differences within class and maximize differences between classes.
  • Based on GVF (Goodness of Variance Fit) - an optimization techniques to minimize the sum of the variance within each of the class.
gvf fisher jenkins algorithms
GVF (Fisher-Jenkins Algorithms)
  • 1) compute the squared deviation of each data
  • Compute SDCM (Squared Deviation, Class Means).
  • Compute GVF = (SDAM - SDCM) / SDAM
  • The goal is to maximize the value of GVF (closer to 1.0 is the better value)
practice
Practice
  • Copy US-states2.xls from g:\4210\data\ to your own folder. (you may need to create a folder under hw and have this file copied to)
  • Compute 5 classes intervals of “Pop90_sqmi” for the following methods
    • Geometric Progression
    • Quantile
    • Equal Interval
    • GVF (use GIS’s range to compute GVF)
practice arcmap
Practice - ArcMap
  • Open a new project and add states.shp from c:\esri\esridata\usa to the layer
  • Plot the US map based on Pop90_sqmi using different methods.
  • Compute GVFs for the four methods.