Which measure combines both precision and recall?

The F₁ score is a harmonic mean of precision and recall, providing a single metric that balances both aspects. Precision indicates the accuracy of the positive predictions made by the model, while recall measures the model's ability to identify all relevant instances. The F₁ score effectively captures the trade-off between these two metrics, especially in situations where there is an imbalanced class distribution. By using the harmonic mean, the F₁ score gives more weight to the lower of the two values, emphasizing the importance of improving both precision and recall simultaneously in a model's performance evaluation. This makes the F₁ score particularly useful in contexts where both false positives and false negatives are costly.

Other measures such as the area under the curve (AUC) primarily assess the performance of a binary classification model across various thresholds but do not combine precision and recall. The receiver operating characteristic (ROC) curve also evaluates model performance but focuses on the trade-offs between true positive rates and false positive rates. Accuracy, while a commonly used metric, does not account for the balance between different types of prediction errors and can be misleading in imbalanced datasets. Therefore, the F₁ score stands out as the most suitable measure for combining precision and recall.