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 results divided by the number of all returned results and r is the number of correct results divided by the number of 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 score at 0.
The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall:
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 measure, which weights recall higher than precision, and the measure, which puts more emphasis on precision than recall.
The F-measure was derived so that "measures the effectiveness of retrieval with respect to a user who attaches β times as much importance to recall as precision". It is based on Van Rijsbergen's effectiveness measure
Their relationship is where .
(as determined by "Gold standard")
|Condition positive||Condition negative|
|True positive||False positive
(Type I error)
Σ True positive
(Type II error)
|True negative||Negative predictive value =
Σ True negative
Σ True positive
Σ True negative
The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance. Earlier works focused primarily on the F1 score, but with the proliferation of large scale search engines, performance goals changed to place more emphasis on either precision or recall and so is seen in wide application.
The F-score is also used in machine learning. Note, however, that the F-measures do not take the true negative rate into account, and that measures such as the Phi coefficient, Matthews correlation coefficient, Informedness or Cohen's kappa may be preferable to assess the performance of a binary classifier.
While the F-measure is the Harmonic mean of Recall and Precision the G-measure is the Geometric Mean of Recall and Precision. Information content corresponds to the Arithmetic Mean of the Information represented by Recall and Precision.
- Precision and recall
- NIST (metric)
- ROUGE (metric)
- Word Error Rate (WER)
- Receiver operating characteristic
- Matthews correlation coefficient
- Uncertainty coefficient, aka Proficiency
- Van Rijsbergen, C. J. (1979). Information Retrieval (2nd ed.). Butterworth.
- POWERS, D.M.W. (February 27, 2011). "EVALUATION: FROM PRECISION, RECALL AND F-MEASURE TO ROC, INFORMEDNESS, MARKEDNESS & CORRELATION". Journal of Machine Learning Technologies 2 (1): 37–63.
- Beitzel., Steven M. (2006). On Understanding and Classifying Web Queries (Ph.D. thesis). IIT. CiteSeerX: 10.1.1.127.634.
- X. Li, Y.-Y. Wang, and A. Acero (July 2008). "Learning query intent from regularized click graphs". Proceedings of the 31st SIGIR Conference.
- See, e.g., the evaluation of the CoNLL 2002 shared task.
- Powers, David M W (2007/2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation". Journal of Machine Learning Technologies 2 (1): 37–63.