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Unit 1: Introduction

20254m

Suppose 10000 patients are tested for flu; out of them, 9000 are actually healthy and 1000 are actually sick. For the sick people, a test was positive for 620 and negative for 380. For the healthy people, the same test was positive for 180 and negative for 8820. Construct a confusion matrix.

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Confusion Matrix Construction (Actual vs Predicted):

Given 10,000 patients: 1,000 actually Sick (Positive class), 9,000 Healthy (Negative).

Test results:

  • Sick: 620 Positive (TP), 380 Negative (FN)
  • Healthy: 180 Positive (FP), 8820 Negative (TN)

Matrix (rows=Actual, cols=Predicted):

Predicted Positive Predicted Negative Row Total
Actually Sick (P) 620 (TP) 380 (FN) 1,000
Actually Healthy (N) 180 (FP) 8820 (TN) 9,000
Col Total 800 9200 10,000

Alternatively Predicted as rows — equivalent transpose; specify.

Derived metrics (optional):

  • Accuracy =(620+8820)/10000=94.4%=(620+8820)/10000=94.4\% (misleading due imbalance)
  • Precision =620/(620+180)=77.5%=620/(620+180)=77.5\%
  • Recall/Sensitivity =620/1000=62%=620/1000=62\%
  • Specificity =8820/9000=98%=8820/9000=98\%
  • False Positive Rate =2%=2\%

Note: Despite high accuracy, recall only 62% — 38% sick missed, critical for medical test. Confusion matrix reveals class imbalance impact better than accuracy alone.

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