F1 score
In statistical analysis of binary classification, the F_{1} score (also Fscore or Fmeasure) 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 returned by the classifier, and r is the number of correct positive results divided by the number of all relevant samples (all samples that should have been identified as positive). The F_{1} score is the harmonic average of the precision and recall, where an F_{1} score reaches its best value at 1 (perfect precision and recall) and worst at 0.
Contents
Etymology
The name Fmeasure is believed to be named after a different F function in Van Rijsbergen's book, when introduced to MUC4. ^{[1]}
Definition
This section needs additional citations for verification. (December 2018) (Learn how and when to remove this template message)

The traditional Fmeasure or balanced Fscore (F_{1} 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 weighs recall higher than precision (by placing more emphasis on false negatives), and the measure, which weighs recall lower than precision (by attenuating the influence of false negatives).
The Fmeasure 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".^{[2]} It is based on Van Rijsbergen's effectiveness measure
 .
Their relationship is where .
The F_{1} score is also known as the Sørensen–Dice coefficient or Dice similarity coefficient (DSC).
Diagnostic testing
This is related to the field of binary classification where recall is often termed as Sensitivity. There are several reasons that the F_{1} score can be criticized in particular circumstances.^{[3]}
True condition  
Total population  Condition positive  Condition negative  Prevalence = Σ Condition positive/Σ Total population  Accuracy (ACC) = Σ True positive + Σ True negative/Σ Total population  
Predicted condition 
Predicted condition positive 
True positive, Power 
False positive, Type I error 
Positive predictive value (PPV), Precision = Σ True positive/Σ Predicted condition positive  False discovery rate (FDR) = Σ False positive/Σ Predicted condition positive  
Predicted condition negative 
False negative, Type II error 
True negative  False omission rate (FOR) = Σ False negative/Σ Predicted condition negative  Negative predictive value (NPV) = Σ True negative/Σ Predicted condition negative  
True positive rate (TPR), Recall, Sensitivity, probability of detection = Σ True positive/Σ Condition positive  False positive rate (FPR), Fallout, probability of false alarm = Σ False positive/Σ Condition negative  Positive likelihood ratio (LR+) = TPR/FPR  Diagnostic odds ratio (DOR) = LR+/LR−  F_{1} score = 2/1/Recall + 1/Precision  
False negative rate (FNR), Miss rate = Σ False negative/Σ Condition positive  Specificity (SPC), Selectivity, True negative rate (TNR) = Σ True negative/Σ Condition negative  Negative likelihood ratio (LR−) = FNR/TNR 
Applications
The Fscore is often used in the field of information retrieval for measuring search, document classification, and query classification performance.^{[4]} Earlier works focused primarily on the F_{1} score, but with the proliferation of large scale search engines, performance goals changed to place more emphasis on either precision or recall^{[5]} and so is seen in wide application.
The Fscore is also used in machine learning.^{[6]} Note, however, that the Fmeasures do not take the true negatives into account, and that measures such as the Matthews correlation coefficient, Informedness or Cohen's kappa may be preferable to assess the performance of a binary classifier.^{[3]}
The Fscore has been widely used in the natural language processing literature, such as the evaluation of named entity recognition and word segmentation.
Criticism
David Hand and others criticize the widespread use of the Fscore since it gives equal importance to precision and recall. In practice, different types of misclassifications incur different costs. In other words, the relative importance of precision and recall is an aspect of the problem.^{[7]}
Difference from Gmeasure
While the Fmeasure is the harmonic mean of Recall and Precision, the Gmeasure is the geometric mean.^{[3]}
See also
 BLEU
 Matthews correlation coefficient
 METEOR
 NIST (metric)
 Precision and recall
 Receiver operating characteristic
 ROUGE (metric)
 Sørensen–Dice coefficient
 Uncertainty coefficient, aka Proficiency
 Word error rate (WER)
References
 ^ Sasaki, Y. (2007). "The truth of the Fmeasure" (PDF).
 ^ Van Rijsbergen, C. J. (1979). Information Retrieval (2nd ed.). ButterworthHeinemann.
 ^ ^{a} ^{b} ^{c} Powers, David M W (2011). "Evaluation: From Precision, Recall and FMeasure to ROC, Informedness, Markedness & Correlation" (PDF). 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; A. Acero (July 2008). Learning query intent from regularized click graphs (PDF). Proceedings of the 31st SIGIR Conference.
 ^ See, e.g., the evaluation of the [1].
 ^ Hand, David. "A note on using the Fmeasure for evaluating record linkage algorithms  Dimensions". app.dimensions.ai. Retrieved 20181208.