# Difference in Proportions of Labels (DPL)
<a name="clarify-data-bias-metric-true-label-imbalance"></a>

The difference in proportions of labels (DPL) compares the proportion of observed outcomes with positive labels for facet *d* with the proportion of observed outcomes with positive labels of facet *a* in a training dataset. For example, you could use it to compare the proportion of middle-aged individuals (facet *a*) and other age groups (facet *d*) approved for financial loans. Machine learning models try to mimic the training data decisions as closely as possible. So a machine learning model trained on a dataset with a high DPL is likely to reflect the same imbalance in its future predictions.

The formula for the difference in proportions of labels is as follows:

        DPL = (qa - qd)

Where:
+ qa = na(1)/na is the proportion of facet *a* who have an observed label value of 1. For example, the proportion of a middle-aged demographic who get approved for loans. Here na(1) represents the number of members of facet *a* who get a positive outcome and na the is number of members of facet *a*. 
+ qd = nd(1)/nd is the proportion of facet *d* who have an observed label value of 1. For example, the proportion of people outside the middle-aged demographic who get approved for loans. Here nd(1) represents the number of members of the facet *d* who get a positive outcome and nd the is number of members of the facet *d*. 

If DPL is close enough to 0, then we say that *demographic parity* has been achieved.

For binary and multicategory facet labels, the DPL values range over the interval (-1, 1). For continuous labels, we set a threshold to collapse the labels to binary. 
+ Positive DPL values indicate that facet *a* is has a higher proportion of positive outcomes when compared with facet *d*.
+ Values of DPL near zero indicate a more equal proportion of positive outcomes between facets and a value of zero indicates perfect demographic parity. 
+ Negative DPL values indicate that facet *d* has a higher proportion of positive outcomes when compared with facet *a*.

Whether or not a high magnitude of DPL is problematic varies from one situation to another. In a problematic case, a high-magnitude DPL might be a signal of underlying issues in the data. For example, a dataset with high DPL might reflect historical biases or prejudices against age-based demographic groups that would be undesirable for a model to learn.