Recall Calculator (Sensitivity)

Analyze your classification model’s performance by calculating recall using inputs from a confusion matrix. Ideal for users of R’s `caret` package and other machine learning frameworks.

What is Recall?

Recall, also known as Sensitivity or the True Positive Rate (TPR), is a fundamental performance metric in machine learning for evaluating classification models. It answers the question: “Of all the actual positive instances, how many did the model correctly identify?”. Recall is crucial in scenarios where failing to identify a positive case has significant consequences. For instance, in medical diagnostics, high recall is vital to ensure that as few sick patients as possible are missed. The term is widely used in many data science toolkits, and this calculator is especially helpful for those calculating recall using the caret package in R, which provides these metrics through its `confusionMatrix` function.

Recall Formula and Explanation

The formula for recall is straightforward and derived from the components of a confusion matrix. It is the ratio of True Positives to the sum of True Positives and False Negatives.

Recall = True Positives / (True Positives + False Negatives)

A perfect model would have zero false negatives, resulting in a recall of 1.0 (or 100%).

Variables Table

The components of a confusion matrix used for calculating recall.

Variable	Meaning	Unit	Typical Range
True Positives (TP)	Correctly identified positive cases.	Count (unitless)	0 to thousands
False Negatives (FN)	Positive cases incorrectly labeled as negative.	Count (unitless)	0 to thousands
False Positives (FP)	Negative cases incorrectly labeled as positive.	Count (unitless)	0 to thousands

Practical Examples

Example 1: Email Spam Detection

Imagine a model that filters spam. An important email incorrectly marked as spam is a False Positive. A spam email that gets into your inbox is a False Negative. For this use case, you might tolerate some spam in your inbox (lower precision) to ensure no important emails are missed (high recall for ‘not spam’ class). Suppose over a day you have 100 actual spam emails.

• Inputs: The model correctly flags 95 of them (TP=95) but misses 5 (FN=5).
• Units: These are counts of emails.
• Result: Recall = 95 / (95 + 5) = 0.95 or 95%. The model successfully recalled 95% of all incoming spam emails. For more details, see our F1-Score Calculator.

Example 2: Medical Screening for a Disease

In medical testing, a False Negative (telling a sick person they are healthy) is often far more dangerous than a False Positive (telling a healthy person they might be sick, requiring further tests). High recall is critical. Consider a screening test applied to 1,000 people, where 20 actually have the disease.

• Inputs: The test correctly identifies 19 of the sick patients (TP=19) but misses 1 (FN=1). It also incorrectly flags 50 healthy people as potentially sick (FP=50).
• Units: These are counts of patients.
• Result: Recall = 19 / (19 + 1) = 0.95 or 95%. The test is 95% sensitive, meaning it correctly identifies 95% of all people who truly have the disease. To understand the trade-off with false alarms, check out our guide to Precision vs. Recall.

How to Use This Recall Calculator

Using this calculator is simple and mirrors the process you’d follow when analyzing a model, perhaps after using a function like `confusionMatrix` from the R caret package.

1. Enter True Positives (TP): Input the total number of items that were actually positive and were correctly classified as positive.
2. Enter False Negatives (FN): Input the total number of items that were actually positive but were incorrectly classified as negative.
3. (Optional) Enter False Positives (FP): For a more complete picture, add the number of negative items wrongly classified as positive. This will enable the Precision and F1-Score calculations.
4. Interpret the Results: The primary result is your model’s recall score. A score closer to 1.0 is better. The intermediate results provide context, like the Precision-Recall Trade-off, which is essential for a balanced model evaluation.

Key Factors That Affect Recall

• Classification Threshold: Lowering the probability threshold for classifying an instance as positive typically increases recall but decreases precision.
• Class Imbalance: In datasets where the positive class is rare, achieving high recall can be challenging and might come at the cost of many false positives.
• Feature Quality: The predictive power of your input features directly impacts the model’s ability to distinguish between classes, thus affecting recall.
• Model Complexity: A more complex model might overfit the training data, leading to poor generalization and potentially lower recall on unseen data.
• Data Preprocessing: Techniques used to clean and prepare data, such as those available in the caret package guide, can significantly influence model performance.
• Choice of Algorithm: Different algorithms have different strengths. Some may be inherently better at achieving high recall for certain types of problems.

Frequently Asked Questions (FAQ)

What’s the difference between recall and precision?

Recall measures how many of the actual positives a model captures, while precision measures how many of the predicted positives are actually correct. There is often an inverse relationship between them.

Is a high recall always good?

Not necessarily. A model that predicts every single instance as “positive” would have a perfect recall of 1.0 but likely terrible precision, making it useless. A balance is needed, which is why we also look at the F1-Score.

What is a good recall score?

This is domain-specific. For critical medical tests, a recall of 99% or higher might be required. For spam filtering, 90-95% might be acceptable.

How does the R `caret` package calculate recall?

The `caret` package’s `confusionMatrix` function automatically computes recall (calling it `Sensitivity`), precision, F1, and other metrics from the predicted and actual values. This calculator helps you manually verify those results or explore scenarios.

Can recall be 0?

Yes. If the model fails to identify any true positive cases (TP = 0), then the recall will be 0.

Can I use this for multi-class problems?

Yes. For multi-class classification, recall is calculated on a per-class basis (one-vs-all). You would use this calculator for one class at a time, defining “positive” as that specific class and “negative” as all other classes.

What are “unitless” values?

The inputs (TP, FN, FP) are counts of data points (e.g., number of images, patients, or emails). They don’t have a physical unit like kilograms or meters. The resulting recall score is a ratio and is also unitless.

When is recall more important than precision?

Recall is more important when the cost of a false negative is high. Examples include fraud detection, cancer screening, and identifying critical safety defects. Missing a positive case is more costly than investigating a false alarm.

Related Tools and Internal Resources

Explore other metrics and concepts to get a full picture of your model’s performance.

• Precision Calculator: Calculate the precision metric to evaluate the rate of false alarms.
• F1-Score Calculator: Find the harmonic mean of precision and recall for a balanced evaluation.
• Accuracy Calculator: Measure the overall correctness of your model.
• Guide to the caret package: Learn more about the powerful tools available in R for machine learning.