# Measures

We provide software implementing the following measures, as found in the literature on algorithmic discrimination. You can find the software in our GitHub repository.

In the following, **positive outcome** is considered as the desired one for a certain candidate in a group, e.g. being granted a loan given a certain credit score (**target score**).
We are continuously expanding the list of available measures.

## Absolute Measures

### Mean Difference

The difference between the target score mean values of the protected vs. unprotected groups.
*No difference = no discrimination*

### Normalized Difference

The mean difference for binary classification normalized by the rate of positive outcomes.
*At a given positive outcome rate, maximum possible discrimination is taken into account*

### Impact Ratio

The ratio of positive outcomes for the protected group over the non-protected group.

### Odds Ratio

The association between exposure and outcome

## Statistical Tests

### Difference of Means *a.k.a. Welch-Test*

For a null hypothesis that the **means of the two groups** (protected and non-protected) are equal.

### Difference in proportions for two groups *a.k.a. Fisher’s exact test*

For a null hypothesis that the **rates of positive outcomes** within the two groups are equal.

## References

Currently we implement measures described in the following references:

Žliobaitė, Indrė. “Measuring discrimination in algorithmic decision making” Data Mining and Knowledge Discovery 31, no. 4 (July 31, 2017): 1060-089. doi:10.1007/s10618-017-0506-1. *bibtex*