1 Chapter 7 – The Choropleth Map Data Classification

2 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.

3 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.

4 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.

5 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

6 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

7 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

8 Geometric Progression Useful technique when frequency of data declines continuously with increasing magnitude a, ar 1, ar 2,...ar n 1) compute common multiplier (a is the lowest value, r is the common multiplier and n is the number of classes use “Xmin x r n = Xmax” to obtain r eg. 118 x r 5 = 790 ( use Area as variable) r = 1.46 So the interval goes from 118, 118x1.46, 118x1.46 2, 118x1.46 3,118x , , , ,

9 Graphic Array Figure 7.11 Class boundaries are identified at places where slopes change remarkably Disadvantage: not suitable for large amount of data

10 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.

11 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)

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13 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)

14 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.