# Specificity difference (SD)
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**Note**  
After careful consideration, we have made the decision to close new customer access to Amazon Sagemaker Clarify, effective 7/30/26. Existing customers can continue to use the service as normal. AWS continues to invest in security and availability improvements for Clarify, but we do not plan to introduce new features. For more information, see [Clarify availability change](clarify-availability-change.md). 

The specificity difference (SD) is the difference in specificity between the favored facet *a* and disfavored facet *d*. Specificity measures how often the model correctly predicts a negative outcome (y'=0). Any difference in these specificities is a potential form of bias. 

Specificity is perfect for a facet if all of the y=0 cases are correctly predicted for that facet. Specificity is greater when the model minimizes false positives, known as a Type I error. For example, the difference between a low specificity for lending to facet *a*, and high specificity for lending to facet *d*, is a measure of bias against facet *d*.

The following formula is for the difference in the specificity for facets *a* and *d*.

        SD = TNd/(TNd \+ FPd) - TNa/(TNa \+ FPa) = TNRd - TNRa

The following variables used to calculated SD are defined as follows:
+ TNd are the true negatives predicted for facet *d*.
+ FPd are the false positives predicted for facet *d*.
+ TNd are the true negatives predicted for facet *a*.
+ FPd are the false positives predicted for facet *a*.
+ TNRa = TNa/(TNa \+ FPa) is the true negative rate, also known as the specificity, for facet *a*.
+ TNRd = TNd/(TNd \+ FPd) is the true negative rate, also known as the specificity, for facet *d*.

For example, consider the following confusion matrices for facets *a* and *d*.

Confusion matrix for the favored facet `a`


| Class a predictions | Actual outcome 0 | Actual outcome 1 | Total  | 
| --- | --- | --- | --- | 
| 0 | 20 | 5 | 25 | 
| 1 | 10 | 65 | 75 | 
| Total | 30 | 70 | 100 | 

Confusion matrix for the disfavored facet `d`


| Class d predictions | Actual outcome 0 | Actual outcome 1 | Total  | 
| --- | --- | --- | --- | 
| 0 | 18 | 7 | 25 | 
| 1 | 5 | 20 | 25 | 
| Total | 23 | 27 | 50 | 

The value of the specificity difference is `SD = 18/(18+5) - 20/(20+10) = 0.7826 - 0.6667 = 0.1159`, which indicates a bias against facet *d*.

The range of values for the specificity difference between facets *a* and *d* for binary and multicategory classification is `[-1, +1]`. This metric is not available for the case of continuous labels. Here is what different values of SD imply:
+ Positive values are obtained when there is higher specificity for facet *d* than for facet *a*. This suggests that the model finds less false positives for facet *d* than for facet *a*. A positive value indicates bias against facet *d*. 
+ Values near zero indicate that the specificity for facets that are being compared is similar. This suggests that the model finds a similar number of false positives in both of these facets and is not biased.
+ Negative values are obtained when there is higher specificity for facet *a* than for facet *d*. This suggests that the model finds more false positives for facet *a* than for facet *d*. A negative value indicates bias against facet *a*.