# Dissimilarity Index

## Introduction

The Dissimilarity Index is a measure of the evenness with which two groups are distributed across the geographic units that make up a larger area of study, measuring how similar or dissimilar two groups are with respect to their geographic spread within a larger region. The index of dissimilarity can also be used as a measure of inequality.

The basic formula for the index of dissimilarity is:

#### $$\frac{1}{2} \sum_{i=1}^N \left| \frac{a_i}{A} – \frac{b_i}{B} \right|$$

where:
$$a_i$$ = the population of group A within the ith area, e.g. within an SA2
$$A$$ = the total population of group A of the large geographic area for which the index of dissimilarity is being calculated. e.g. within a GCCSA
$$b_i$$ = the population of group B within the ith area
$$B$$ = the total population of group B of the large geographic entity for which the index of dissimilarity is being calculated.

The Dissimilarity Index is applicable to any categorical variable (whether demographic or not) and because of its simple properties is useful for input into multidimensional scaling and clustering programs. It has been used extensively in the study of social mobility to compare distributions of origin (or destination) occupational categories.

DI values close to 1 indicate a high dissimilarity, and DI values close to zero indicate low dissimilarity (high similarity) in the geographic spread of the two variables.

## Inputs

To show the Dissimilarity Index in action, we will compare the geographic distribution of the population within two different age groups (25 to 29 year olds, and 65 years and over) across Melbourne by SA2.

To do this:

• Select Melbourne GCCSA as your area
• Select SA2 Age Distribution – Persons as your dataset, checking the Persons 25 to 29 Years – Count and Persons 65 Years and Over – Count attributes

Once you have downloaded this dataset, open the Dissimilarity Index tool (Tools → Spatial Statistics → Dissimilarity Index) and enter the parameters as shown in the image below. Once you have entered your parameters, click Add and Run to execute the tool

[Click to Enlarge]

## Outputs

Once you have run the tool, click on the Display button in the pop up window that appears. This will bring up a simple text window like the one below, which indicates some dissimilarity between the geographic spread of 25-29 year olds and 65+ year olds in Melbourne

[Click to Enlarge]