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A two-class classification model was evaluated on 200 test samples, and its confusion matrix shows 45 true positives (TP), 5 false positives (FP), 45 false negatives (FN) and 105 true negatives (TN). Which pair of precision and recall is correct?

  1. APrecision 0.50, recall 0.90
  2. BPrecision 0.75, recall 0.50
  3. CPrecision 0.90, recall 0.50
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Answer: C. Precision 0.90, recall 0.50

Precision is the fraction of items predicted positive that are actually positive: TP ÷ (TP + FP) = 45 ÷ 50 = 0.90. Recall is the fraction of actually positive items that were predicted positive: TP ÷ (TP + FN) = 45 ÷ 90 = 0.50. This model is almost always right when it says positive, but it misses half of the positives. Accuracy is (45 + 105) ÷ 200 = 0.75.

  • A. Precision and recall are swapped.
  • B. 0.75 is the accuracy (the fraction of all predictions that are correct), not the precision.
  • C. Correct. Precision is 45 ÷ 50 = 0.90 and recall is 45 ÷ 90 = 0.50.
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