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:

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} .