Precision and Recall

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

F-measure (or F1 score) is the harmonic mean of precision and recall

$$ F = \frac{2 (\text{precision} \times \text{recall})}{(\text{precision} + \text{recall})} $$

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