# Disparate Impact (DI)


The difference in positive proportions in the predicted labels metric can be assessed in the form of a ratio.

The comparison of positive proportions in predicted labels metric can be assessed in the form of a ratio instead of as a difference, as it is with the [Difference in Positive Proportions in Predicted Labels (DPPL)](clarify-post-training-bias-metric-dppl.md). The disparate impact (DI) metric is defined as the ratio of the proportion of positive predictions (y’ = 1) for facet *d* over the proportion of positive predictions (y’ = 1) for facet *a*. For example, if the model predictions grant loans to 60% of a middle-aged group (facet *a*) and 50% other age groups (facet *d*), then DI = .5/.6 = 0.8, which indicates a positive bias and an adverse impact on the other aged group represented by facet *d*.

The formula for the ratio of proportions of the predicted labels:



        DI = q'd/q'a

Where:
+ q'a = n'a(1)/na is the predicted proportion of facet *a* who get a positive outcome of value 1. In our example, the proportion of a middle-aged facet predicted to get granted a loan. Here n'a(1) represents the number of members of facet *a* who get a positive predicted outcome and na the is number of members of facet *a*. 
+ q'd = n'd(1)/nd is the predicted proportion of facet *d* a who get a positive outcome of value 1. In our example, a facet of older and younger people predicted to get granted a loan. Here n'd(1) represents the number of members of facet *d* who get a positive predicted outcome and nd the is number of members of facet *d*. 

For binary, multicategory facet, and continuous labels, the DI values range over the interval [0, ∞).
+ Values less than 1 indicate that facet *a* has a higher proportion of predicted positive outcomes than facet *d*. This is referred to as *positive bias*.
+ A value of 1 indicates demographic parity. 
+ Values greater than 1 indicate that facet *d* has a higher proportion of predicted positive outcomes than facet *a*. This is referred to as *negative bias*.