AI Glossary / Causal inference and experimentation / Intermediate
False negative rate
Definition
False negative rate is the proportion of actual positive cases that a binary classifier incorrectly labels negative. It is calculated as false negatives divided by all actual positives: FN/(TP + FN). It is also called the miss rate and equals one minus recall or sensitivity for the same positive class and evaluation population. A lower value means fewer positive cases are missed, but it does not describe how many negative cases are falsely flagged.
What it means
The denominator is the set of cases that truly have the condition or property being detected. If the positive class means “requires specialist review”, a false negative is a case that requires review but is not flagged. The rate asks how often such cases are overlooked. It does not ask how trustworthy a negative prediction is; that is a different conditional question whose denominator consists of predicted negatives rather than actual positives.
How it works
Define the positive class and reference labels, then apply a specified decision threshold to the model's scores. Count actual positives that are correctly flagged as TP and actual positives missed as FN. Divide FN by TP + FN. Record the number of positive cases because the estimate can be unstable when positives are rare. If there are no actual positives, the empirical rate is undefined and needs a stated reporting convention. Examine the rate across relevant case types and thresholds, alongside false positive rate and workload counts.
Three practical examples
- Defect inspection: measure the fraction of genuinely faulty items that pass through without being flagged.
- Document review: assess how often records needing specialist attention are incorrectly routed as routine.
- Search filtering: evaluate how many genuinely relevant items are excluded by a binary eligibility or relevance decision.
Think of it this way
Think of a net intended to catch a particular kind of object. The miss rate counts the target objects that slip through, divided by all target objects presented. It says nothing about unwanted objects caught by the net. The analogy clarifies the denominator, but real classifiers may face changing inputs and imperfect reference labels rather than a fully observable set of objects.
Worked example
A fictional evaluation includes 200 items that truly require review and 800 routine items. The model flags 170 of the review items and misses 30, while also flagging 40 routine items. False negative rate is 30/200 = 15%. Recall is 170/200 = 85%, confirming that the two sum to 100%.
There are 760 correctly unflagged routine items, so the predicted-negative group contains 760 + 30 = 790 items. The fraction of predicted negatives that actually require review is 30/790, approximately 3.80%. That is the false omission rate, not the false negative rate. Both describe the same 30 misses but answer different questions. If a lower threshold reduces misses to 10 while increasing routine flags to 100, false negative rate falls to 10/200 = 5%. The improvement comes with extra review work, which must be examined rather than hidden behind the lower miss rate.
Illustrative case study
A fictional quality team sees a low overall miss rate and assumes its detector is reliable across all defect types. A breakdown shows that common visible defects are usually found, but a small category of subtle defects is often missed. The team reviews labeling quality, sample size, and image conditions for that category. It expands the evaluation before changing the detector. The overall rate remains useful, but category-specific evidence is necessary to understand where missed positives are concentrated.
Common misconceptions and mistakes
False negative rate is not the probability that a negative prediction is wrong. It is not the overall error rate, because actual negatives are excluded from its denominator. Lowering the decision threshold can reduce misses without improving the underlying ranking model and can increase false positives. A zero observed miss rate on a small positive sample does not prove a zero population miss rate. Changing the definition of a positive case or the tested population can also change the meaning of the reported rate.
Business use
Use false negative rate when overlooked positive cases are an important failure mode. Report the actual number of misses and the number of positives tested. Pair the rate with false positive counts, precision, and the consequences of both error types. Keep evaluation labels independent of the model where possible, and investigate uncertain labels. If the system abstains or sends uncertain cases for review, describe how those outcomes enter the metric. Reassess the rate when input conditions or positive-case composition changes.
People also ask
Does a 5% false negative rate mean 5% of all predictions are wrong?
No. It means 5% of actual positive cases are missed under the evaluation rule.
Can false negative rate be reduced to zero by flagging everything?
Yes for binary decisions when positives exist, but that creates false positives for every actual negative and is usually not a useful solution.
Is miss rate always the same as one minus recall?
Yes when both use the same positive definition, cases, weighting, and treatment of outcomes.
Check your understanding
In the worked example, why is 30 divided by 200 rather than by 790?
Answer: False negative rate conditions on actual positives, and there are 200 of them. Dividing by 790 instead conditions on negative predictions and calculates a different measure, the false omission rate.
Related terms
- False negative
- Recall
- Confusion matrix
- False positive rate
- Positive class
- sensitivity
- miss rate
- false omission rate
- threshold selection
- selective prediction
Learn next
Build a confusion matrix and circle the row containing actual positives. Calculate the fraction missed, then compare it with the fraction of negative predictions that are wrong. Next study precision-recall and DET curves so a lower miss rate can be interpreted together with the extra false alarms and review workload it may create.
More in Causal inference and experimentation
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- F 1 - F1, sometimes written F 1 or F1 score, combines precision and recall through their harmonic mean.
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Sources
Scikit-learn, recall_score: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.recall_score.html Scikit-learn, confusion_matrix: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html Scikit-learn, detection error tradeoff example: https://scikit-learn.org/stable/auto_examples/model_selection/plot_det.html
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