Sensitivity and Specificity

Although similar, sensitivity and specificity are not the same as precision and recall. Here are the definitions:

In the cancer example, sensitivity and specificity are the following:

• Sensitivity: Of all the people with cancer, how many were correctly diagnosed?
• Specificity: Of all the people without cancer, how many were correctly diagnosed?

And precision and recall are the following:

• Recall: Of all the people who have cancer, how many did we diagnose as having cancer?
• Precision: Of all the people we diagnosed with cancer, how many actually had cancer?

From here we can see that Sensitivity is Recall, and the other two are not the same thing.

Trust me, we also have a hard time remembering which one is which, so here's a little trick. If you remember from Luis's Evaluation Metrics section, here is the [confusion matrix](- Confusion Matrix:

Now, sensitivity and specificity are the rows of this matrix. More specifically, if we label

• TP: (True Positives) Sick people that we correctly diagnosed as sick.
• TN: (True Negatives) Healthy people that we correctly diagnosed as healthy.
• FP: (False Positives) Healthy people that we incorrectly diagnosed as sick.
• FN: (False Negatives) Sick people that we incorrectly diagnosed as healthy.

then:

Sensitivity = \frac{TP}{TP + FN}

and

Specificity = \frac{TN}{TN + FP}.

And precision and recall are the top row and the left column of the matrix:

Recall = \frac{TP}{TP + FN}

and

Precision = \frac{TP}{TP + FP} .