# Dissimilarity index

## Definition

The index of dissimilarity is defined as one-half of the sum of absolute differences in proportions between two populations of interest (e.g. teachers and pupils) across all geographic sub-divisions of the country (administrative division, eg. Province, State, District).

## Calculation method

Calculate the proportion (as a share of total) of each population of interest (e.g. pupils and teachers) for each administrative sub-division. Sum up absolute differences between these proportions and divide by two.

## Data required

Number of pupils and teachers at sub-national level by each level of education, or any other population of interest.

## Data source

Administrative data from schools and other organized learning centers.

## Interpretation

Value of DI can be interpreted as the proportion of individuals from population i (e.g. teachers) that would need to be reallocated in order to obtain an even distribution of population i (e.g. teachers) with regard to the distribution of population j (e.g. pupils) across administrative divisions. For example, a dissimilarity index of 0.2 for the distribution of teachers against the distribution of pupils means that 20% of the total number of teachers would need to be redistributed across administrative divisions to equalize the distribution of teachers and the distribution of pupils across all administrative divisions.The value of DI is comprised between 0 and 1. It is minimized (0) when both distributions are perfectly equal. The higher the value of DI the higher the degree of disparity between the distribution of the two populations.

## Limitations

As a measure of equity, the dissimilarity index can only be used to report on horizontal equity i.e. when administrative units are considered to have the same characteristics. It doesn’t indicate whether the distribution is actually biased towards wealthiest or poorest regions for instance.

## Purpose

The index of dissimilarity is generally used to describe the (un-)evenness with which two mutually exclusive populations are distributed across all sub-divisions of a given geographic area. For instance, the index of dissimilarity quantifies the magnitude of inequality between the distribution of teachers and the distribution of pupils across provinces in a given country.

## Types of disaggregation

By level of education and by type of institutions