- Year not given
Measures from cancer confusion matrix
Short answer
Accuracy 96.5%, error rate 3.5%, sensitivity/recall/TPR 30%, specificity/TNR 98.56%, precision/PPV 39.1%, NPV 97.85%, FPR 1.44%, FNR 70%.
Given the following confusion matrix, determine Accuracy, Error rate, Sensitivity, Specificity, Precision, Recall, Positive Predictive Value and Negative Predictive Value, TPR, TNR, FPR, FNR of the classifier model.
| Actual \ Predicted | cancer = yes | cancer = no |
|---|---|---|
| cancer = yes | 90 | 210 |
| cancer = no | 140 | 9560 |
Positive class = cancer = yes (rows are actual, columns predicted):
TP = 90, FN = 210, FP = 140, TN = 9560. Total = 90 + 210 + 140 + 9560 = 10000. Actual cancer = 300; actual no cancer = 9700.
| Measure | Formula | Calculation | Value |
|---|---|---|---|
| Accuracy | (TP + TN)/total | (90 + 9560)/10000 | 0.965 (96.5%) |
| Error rate | (FP + FN)/total | 350/10000 | 0.035 (3.5%) |
| Sensitivity = Recall = TPR | TP/(TP + FN) | 90/300 | 0.300 |
| Specificity = TNR | TN/(TN + FP) | 9560/9700 | 0.9856 |
| Precision = PPV | TP/(TP + FP) | 90/230 | 0.391 |
| NPV | TN/(TN + FN) | 9560/9770 | 0.9785 |
| FPR | FP/(FP + TN) | 140/9700 | 0.0144 |
| FNR | FN/(FN + TP) | 210/300 | 0.700 |
Answer: accuracy 96.5%, error rate 3.5%, sensitivity = recall = TPR = 30%, specificity = TNR = 98.56%, precision = PPV = 39.1%, NPV = 97.85%, FPR = 1.44%, FNR = 70%.
Comment: the accuracy is high only because 97% of the records are non-cancer (class imbalance). The classifier misses 70% of the real cancer cases, so for this problem sensitivity (recall) is the important measure and this model is poor.
✓ Answer checked by Claude Opus 5.5 (high effort)
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