Is the F1 score the harmonic mean of precision, recall and accuracy?

Question

The F1 Score is a metric defined as the harmonic mean of precision, recall, and accuracy.

Accepted Answer

False

False. The F1 score is the harmonic mean of precision and recall only: F1 = 2 · precision · recall / (precision + recall). Accuracy is not part of the formula.

The harmonic mean is used because it is dragged down by the smaller of the two numbers. A classifier with precision 1.0 and recall 0.1 has an arithmetic mean of 0.55 but an F1 of about 0.18, which reflects how poorly it actually finds the positive class.

Accuracy is left out on purpose. F1 is mostly used on imbalanced problems such as fraud or disease detection, where accuracy is misleading: predicting the majority class every time can score 99% accuracy while catching nothing. When precision and recall are not equally important, the F-beta score weights recall beta times as much as precision.

The F1 Score is a metric defined as the harmonic mean of precision, recall, and accuracy.

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