False Negative Rate (FNR) Calculator
Number of positive cases incorrectly identified as negative.
Number of positive cases correctly identified as positive.
Please enter valid non-negative numbers for both fields. Total positive cases cannot be zero.
False Negative Rate (FNR):
0.00%
Sensitivity (Recall):
0.00%
Total Positive Cases:
0
Understanding False Negative Rate
The False Negative Rate (FNR) is a crucial metric in statistics, machine learning, and medical diagnostics. It measures the proportion of actual positive cases that were incorrectly classified as negative by a test or model. In statistical hypothesis testing, this is known as a Type II error ($\beta$).
Simply put, it answers the question: "Of all the people who actually have the condition, what percentage did the test miss?"
FNR = FN / (FN + TP)
Where:
- FN (False Negatives): The number of actual positive cases that the test missed.
- TP (True Positives): The number of actual positive cases that the test correctly detected.
- FN + TP: Represents the total number of actual positive cases.
Why is FNR Important?
The significance of the False Negative Rate depends heavily on the context:
- Medical Testing: A high FNR is dangerous. If a test for a serious disease has a high false negative rate, many patients who have the disease will be told they are healthy, delaying necessary treatment.
- Cybersecurity: In intrusion detection, a false negative means a security breach occurred but the system failed to raise an alarm.
- Quality Control: A false negative in manufacturing might mean a defective product is shipped to a customer.
Relationship with Sensitivity
False Negative Rate is the complement of Sensitivity (also known as Recall or True Positive Rate). If a test has a sensitivity of 95%, it means it correctly identifies 95% of positive cases. Consequently, the False Negative Rate would be 5%.
Formula: Sensitivity = 1 – FNR
Example Calculation
Imagine a medical study screening 100 patients who are known to have a specific virus:
- The test correctly identifies 90 patients as having the virus (90 True Positives).
- The test incorrectly tells 10 patients they are healthy (10 False Negatives).
Step 1: Calculate Total Positives = 90 + 10 = 100.
Step 2: Calculate FNR = 10 / 100 = 0.10.
Result: The False Negative Rate is 10%.