Step by Step
TP
True Positive — predicted yes, was yes ✓
The model predicted the positive class, and it was correct — a genuine "win" on the report card.
Example: correctly flagging an actual spam email as spam.
FP
False Positive — predicted yes, was no ✗ (Type I error)
The model predicted the positive class, but it was wrong — a false alarm, marked as a Type I error on the report card.
Example: incorrectly flagging a legitimate email as spam.
FN
False Negative — predicted no, was yes ✗ (Type II error)
The model predicted the negative class, but it was wrong — a missed detection, marked as a Type II error on the report card.
Example: failing to catch an actual spam email, letting it through to the inbox.
TN
True Negative — predicted no, was no ✓
The model predicted the negative class, and it was correct — another genuine "win" on the report card.
Example: correctly leaving a legitimate email in the inbox, not flagged as spam.
Applied Walkthrough
1
A confusion matrix is laid out with predicted positive/negative as columns and actual positive/negative as rows, with TP conventionally placed in the top-left when positive is the class of interest.
2
Reading straight down the diagonal (TP and TN) shows all the model's correct predictions — its report card "wins."
3
Reading off the diagonal (FP and FN) shows all the model's mistakes, split into two distinct error types — false alarms versus missed detections.
4
Every other evaluation metric (precision, recall, F1, accuracy) is calculated by combining these same four report-card numbers in different ways, which is why correctly reading the matrix layout is the essential foundation for everything else.
Exam Application
Exams test whether you can correctly read a confusion matrix's layout and identify all four cells given raw numbers, and whether you remember the standard convention that the diagonal represents correct predictions while the off-diagonal cells represent the two distinct error types.
⚠ Common Trap
The most common trap is misreading which axis represents predicted versus actual values, or mixing up which off-diagonal cell is FP versus FN. A reliable check: the second word in the label ("Positive" or "Negative") always tells you what the model predicted.
✓ Quick Self-Check
1. What do the diagonal cells (TP and TN) of a confusion matrix represent?
All the model's correct predictions.
Tap to reveal / hide
2. What do the off-diagonal cells (FP and FN) represent?
The model's two distinct types of mistakes — false alarms and missed detections.
Tap to reveal / hide
3. What is another name for a False Positive?
A Type I error.
Tap to reveal / hide
4. What is another name for a False Negative?
A Type II error.
Tap to reveal / hide
5. What do all other evaluation metrics like precision, recall, F1, and accuracy derive from?
The same four confusion matrix numbers: TP, FP, FN, and TN.
Tap to reveal / hide