# Dissimilarity Index

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.

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

### SET UP

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.

• Select Greater Melbourne as your area.
• Select SA2 Age Distribution – Persons 2013 as your dataset, selecting the following variables:
• Persons 25 to 29 Years – Count
• Persons 65 Years and Over – Count

### Inputs

Once you have set up the area and dataset, open the Dissimilarity Index tool (Tools → Indices → Dissimilarity Index) and enter the parameters as described below.

• Dataset Input: Select the dataset that you would like to run the Dissimilarity Index tool for. Select SA2 Age Distribution – Persons 2013.
• Variable One: Select one variable to use in the tool. Select Persons 25 to 29 Years – Count.
• Variable Two: Select the second variable to compare against the first. Select Persons 25 to 29 Years – Count.

Once you have entered your parameters, click Run Tool.

### Outputs

Once you have run the tool, click on the Display Output button in the pop-up window that appears. This will bring up a simple text window like the one below.

Our output indices some dissimilarity between the geographic spread of 25-29 year olds and 65+ year olds in Melbourne.

### Looking for Spatial Data?

You can browse the AURIN Data Discovery: