Confusion Matrix & Metrics

Question 1

Which metric is best when False Negatives are very costly (e.g., detecting a disease)?

Accepted Answer

Recall — Recall (Sensitivity) measures the proportion of actual positives correctly identified. High recall is maximizing the capture of positive cases.

Question 2

What does Precision measure?

Accepted Answer

Of positive predictions, how many were truly positive — Precision gives the accuracy of positive predictions: TP / (TP + FP).

Question 3

In a confusion matrix, a False Positive (Type I error) is when the model…

Accepted Answer

Predicts positive but the truth is negative — A False Positive is a negative case wrongly flagged as positive — e.g. a legitimate email marked as spam.

Question 4

A False Negative (Type II error) is when the model…

Accepted Answer

Predicts negative but the truth is positive — A False Negative misses a true positive — e.g. failing to detect a disease that is actually present.

Question 5

Precision is defined as…

Accepted Answer

TP / (TP + FP) — Precision = TP/(TP+FP): of everything predicted positive, how many truly are. It answers 'when I say positive, how often am I right?'

Question 6

Recall (sensitivity) is defined as…

Accepted Answer

TP / (TP + FN) — Recall = TP/(TP+FN): of all actual positives, how many were caught. It answers 'how many real positives did I find?'

Question 7

The F1 score is…

Accepted Answer

The harmonic mean of precision and recall — F1 = 2·(P·R)/(P+R). The harmonic mean punishes imbalance, so F1 is high only when BOTH precision and recall are high.

Question 8

Why can ACCURACY be misleading on imbalanced data?

Accepted Answer

Majority-class prediction can score high accuracy — With 99% negatives, predicting 'negative' always gives 99% accuracy yet zero recall — the 'accuracy paradox'. Use precision/recall/F1 instead.

Question 9

For cancer screening, which metric usually matters MOST?

Accepted Answer

Recall, so as to catch true positives — Missing a real cancer (False Negative) is far costlier than a false alarm, so high recall (sensitivity) is prioritized.

Question 10

For a spam filter that must not lose real email, you'd prioritize…

Accepted Answer

Just plain precision — A False Positive (real email in spam) is costly, so high precision matters more — you tolerate some spam slipping through to avoid losing real mail.

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