Precision and Recall

The precision and the recall are two statistical values which make it possible to characterize the differences between 2 sets of elements: the calculated/selected set (to be evaluated/compared) and the expected set (reference/gold standard).

Precision is the ratio of the number of common elements relative to the size of the calculated set. Precision is also known as positive predictive value.

The reminder is the ratio of the number of common elements relative to the size of the expected set. The recall is also known as true positive rate or sensitivity.

For more statistical data, see the Confusion Matrix page.

For a search, the precision is the ratio of the number of pertinent items found over the total number of items found.

$$ \text{Precision}=\frac{|\{\text{Relevant items}\}\cap\{\text{Retrieved items}\}|}{|\{\text{Retrieved items}\}|} $$

Example: The expected (reference) set is A,B,C,D,E (5 items) and the retrieved/found set are B,C,D,F (4 items). The set of expected items retrieved is B,C,D (3 common items). The precision is $$ P = \frac{3}{4} = 75\% $$

The recall is the ratio of the number of pertinent items found over the total number of relevant items.

$$ \text{Recall}=\frac{|\{\text{Relevant items}\}\cap\{\text{Retrieved items}\}|}{|\{\text{Relevant items}\}|} $$

Example: The reference expected set is A,B,C,D,E (5 items), and the retrieved/found set is B,C,D,F (4 items). The set of expected items retrieved is B,C,D (3 common items). The recall is $$ R = \frac{3}{5} = 60\% $$

In statistics, F-measure (or F1 score) is the harmonic mean of precision $ P $ and recall $ R $

$$ F = \frac{2 (P \times R)}{(P + R)} $$

The following diagram includes precision, recall, true positive, false positive, true negative and false negative (source wikipedia)