Chapter 7 – The Choropleth Map

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# Chapter 7 – The Choropleth Map - PowerPoint PPT Presentation

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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### 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Figure 7.11
• Class boundaries are identified at places where slopes change remarkably
• Disadvantage: not suitable for large amount of data
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)
• 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
• 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
• 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.