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Calculate Number of True Positives

Reviewed by Calculator Editorial Team

In binary classification models, a true positive is a correct prediction of the positive class. This calculator helps you determine the number of true positives based on your model's performance metrics.

What is a true positive?

A true positive occurs when a classification model correctly identifies an instance as belonging to the positive class. In medical testing, for example, a true positive would be when a test correctly identifies a patient as having a disease.

True positives are one of the four possible outcomes in a binary classification system:

  • True Positive (TP): Correctly identified positive cases
  • False Positive (FP): Incorrectly identified positive cases
  • True Negative (TN): Correctly identified negative cases
  • False Negative (FN): Incorrectly identified negative cases

Key Concept

The confusion matrix is a table that summarizes the performance of a classification model by showing these four outcomes.

Formula for true positives

The number of true positives (TP) can be calculated using the following formula:

Formula

TP = (Sensitivity × (TP + FN)) / (Sensitivity + Specificity)

Where:

  • Sensitivity = TP / (TP + FN)
  • Specificity = TN / (TN + FP)

Alternatively, if you know the total number of positive cases and the false positive rate, you can use:

Alternative Formula

TP = Total Positive Cases - FP

Worked example

Let's calculate the number of true positives for a model with the following metrics:

  • Total positive cases: 100
  • False positive rate: 5%

Using the alternative formula:

  1. Calculate false positives: 5% of 100 = 5
  2. Calculate true positives: 100 - 5 = 95

So, the model has 95 true positives.

Interpreting results

A high number of true positives indicates your model is good at identifying positive cases. However, you should also consider:

  • False positives: Cases incorrectly identified as positive
  • False negatives: Cases incorrectly identified as negative
  • Precision: TP / (TP + FP)
  • Recall: TP / (TP + FN)

These metrics together provide a complete picture of your model's performance.

FAQ

What is the difference between true positives and false positives?

A true positive is a correct prediction of the positive class, while a false positive is an incorrect prediction of the positive class.

How do I calculate true positives from a confusion matrix?

The true positives are the values in the top-left cell of the confusion matrix.

What is a good number of true positives?

A good number depends on your specific application and the trade-offs between false positives and false negatives.