False Positive Rate Calculator
Understanding the False Positive Rate (FPR)
In binary classification, a confusion matrix is a fundamental tool for evaluating the performance of a model. It breaks down the predictions made by the model into four categories: True Positives (TP), True Negatives (TN), False Positives (FP), and False Negatives (FN).
What are False Positives?
A False Positive (FP) occurs when the model incorrectly predicts the positive class when the actual class is negative. In simpler terms, it's a "Type I error." For example, in a medical test, a false positive means the test indicates a disease is present when it actually is not. In spam detection, a false positive means a legitimate email is flagged as spam.
What are True Negatives?
A True Negative (TN) occurs when the model correctly predicts the negative class when the actual class is negative. This is a correct "negative" prediction.
Calculating the False Positive Rate (FPR)
The False Positive Rate (FPR), also known as the fall-out or probability of false alarm, quantifies the proportion of actual negatives that were incorrectly identified as positive. It is a crucial metric when the cost of a false positive is significant.
The formula for FPR is:
FPR = FP / (FP + TN)
Where:
- FP is the number of False Positives.
- TN is the number of True Negatives.
A lower FPR indicates that the model is less likely to incorrectly flag actual negative instances as positive, which is desirable in many applications.
Example Calculation
Let's consider a scenario where a disease detection model is evaluated:
- The model correctly identified 800 patients who did not have the disease as negative (True Negatives = 800).
- The model incorrectly identified 50 patients who did not have the disease as positive (False Positives = 50).
Using the FPR formula:
FPR = 50 / (50 + 800)
FPR = 50 / 850
FPR ≈ 0.0588
This means that approximately 5.88% of the individuals who did not have the disease were incorrectly flagged as having the disease by the model.