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Comparing Distributions Heterogeneity : 

Comparing Distributions Heterogeneity Jon Anson Sylvie Gadeyne

Distributions of Origin Groups in Brussels Communes: 

Distributions of Origin Groups in Brussels Communes

Chart: 

Chart

Problem: Communes are of different sizes: 

Problem: Communes are of different sizes So convert to percentages within communes

Graphic representation: 

Graphic representation

Measuring Heterogeneity : 

Measuring Heterogeneity IC: Index of Concentration Take the proportion in each category pi 2. Square it pi2

Example: Brussels Capital Region: 

Example: Brussels Capital Region

Measuring Heterogeneity : 

Measuring Heterogeneity IC: Index of Concentration 3. Sum the squares

Brussels Capital Region (Continued): 

Brussels Capital Region (Continued) 0.485 0.262

Measuring Heterogeneity : 

Measuring Heterogeneity IC: Index of Concentration 4. At maximum concentration, IC=1 5. At minimum IC=1/k Note: Value of IC varies with number of categories, k

Some other communes: 

Some other communes

Comparing Distributions Duncan’s Index of Dissimilarity: 

Comparing Distributions Duncan’s Index of Dissimilarity For each category, take absolute differences between the proportion in each group

Example: St. Gillis vs Elsene: 

Example: St. Gillis vs Elsene

Comparing Distributions Duncan’s Index of Dissimilarity: 

Comparing Distributions Duncan’s Index of Dissimilarity 2. Sum the absolute differences 3. Divide by 2 4. D is the proportion (or percentage) in each group which has to be reallocated to give the same distribution as in the other group

Example: St. Gillis vs Elsene: 

Example: St. Gillis vs Elsene Sum = 38.99 D = 19.5

Example: Watermaal vs St. Joost: 

Example: Watermaal vs St. Joost D = 41.6