F-score

In statistical analysis of binary classification, the F₁ score (also F-score or F-measure) is a measure of a test's accuracy. It considers both the precision p and the recall r of the test to compute the score: p is the number of correct positive results divided by the number of all positive results, and r is the number of correct positive results divided by the number of positive results that should have been returned. The F₁ score can be interpreted as a weighted average of the precision and recall, where an F₁ score reaches its best value at 1 and worst at 0.

The traditional F-measure or balanced F-score (F₁ score) is the harmonic mean of precision and recall — multiplying the constant of 2 scales the score to 1 when both recall and precision are 1:

The general formula for positive real β is:

The formula in terms of Type I and type II errors:

Two other commonly used F measures are the ${\displaystyle F_{2}}$ measure, which weighs recall higher than precision (by placing more emphasis on false negatives), and the ${\displaystyle F_{0.5}}$ measure, which weighs recall lower than precision (by attenuating the influence of false negatives).

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