- Year not given
Measures from confusion matrix (152, 130)
Short answer
Accuracy 78.2%, error rate 21.8%, sensitivity/recall/TPR 53.9%, specificity/TNR 87.7%, precision/PPV 63.3%, NPV 82.9%, FPR 12.3%, FNR 46.1%.
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 | + ve | - ve |
|---|---|---|
| + ve | 152 | 130 |
| - ve | 88 | 630 |
Taking "+ve" as the positive class (rows are actual, columns are predicted):
TP = 152, FN = 130, FP = 88, TN = 630. Total = 152 + 130 + 88 + 630 = 1000. Actual positives P = 282, actual negatives N = 718. Predicted positives = 240, predicted negatives = 760.
| Measure | Formula | Calculation | Value |
|---|---|---|---|
| Accuracy | (TP + TN)/total | (152 + 630)/1000 = 782/1000 | 0.782 (78.2%) |
| Error rate | (FP + FN)/total | 218/1000 | 0.218 (21.8%) |
| Sensitivity = Recall = TPR | TP/(TP + FN) | 152/282 | 0.539 |
| Specificity = TNR | TN/(TN + FP) | 630/718 | 0.877 |
| Precision = PPV | TP/(TP + FP) | 152/240 | 0.633 |
| NPV | TN/(TN + FN) | 630/760 | 0.829 |
| FPR | FP/(FP + TN) | 88/718 | 0.123 |
| FNR | FN/(FN + TP) | 130/282 | 0.461 |
Checks: TPR + FNR = 1 and TNR + FPR = 1; error rate = 1 − accuracy.
The F₁ score = 2·0.633·0.539/(0.633 + 0.539) = 0.582.
Answer: accuracy 78.2%, error rate 21.8%, sensitivity = recall = TPR = 53.9%, specificity = TNR = 87.7%, precision = PPV = 63.3%, NPV = 82.9%, FPR = 12.3%, FNR = 46.1%. The classifier finds only about half of the positive cases.
✓ Answer checked by Claude Opus 5.5 (high effort)
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