# Diversity Index

## Introduction

A diversity index measures the degree of specialisation or alternatively the degree of diversity across attributes within a spatial unit. This allows spatial units to be compared as to the mix of the characteristics being measured.
The diversity index is calculated as follows (Tidswell and Barker, 1971):

$$SDI = \sqrt{p_{1}^2+p_{2}^2\ldots+p_{n}^2}$$

Where $$p_{n}$$ is the variable of interest as a proportion of the total of the $$n$$ variables, for the spatial unit. A common use of the diversity index in economics is to measure the industrial diversity in regions, where $$p_{n}$$ for a particular region becomes employment in industry n as a proportion of total employment in the region.

The diversity index for a particular region can range from 0 to 1, where a score approaching 0 indicates an increasing degree of diversity and a score approaching 1 indicates an increasing degree of specialisation. Determination of whether a region has a high or low diversity index is done by comparing the diversity index scores across all regions.

## Inputs

To illustrate this tool in use, we will look at employment diversity in LGAs across Tasmania in 2011. To do this:

• Select Tasmania as your area
• Select LGA Industry Sectors 2001 – 2006 – 2011 for Australia, selecting all variables

Once you have added this dataset to your cart, open the Diversity Index tool (Tools → Indices → Diversity Index) and enter the parameters as shown in the image below (these are also shown under the image)

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• Dataset Input: the dataset that contains the variables you would like to include. In this instance, select LGA Industry Sectors 2001 – 2006 – 2011 for Australia
• Key Column: the column containing the unique identifier for each area. In this instance, select LGA Code
• Variables: the variables you would like to be included in the calculation of the index. In this instance, select all variables that end in XXX (2011except Total Persons (2011) and Inadequately described & not stated (2011)

Once you have added the parameters, click Add and Run to execute the tool

## Outputs

Once your tool has run, click on the Display button that appears on the pop up dialogue box. This will open a table that looks something like the image below. The Diversity Index is found at the far right of the table.

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You can create a choropleth of the dataset using a sequential palette, making sure to reverse the palette to show that the lighter colours reflect the lack of diversity (higher numbers). It should look something like below, showing that the Central Highlands and West Coast LGAs have the lowest employment diversity

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