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This false positive calculator will help you determine the proportion of tests that incorrectly diagnosed healthy people as sick. In what follows we will:

  • Briefly recall the necessary definitions related to diagnostic tests;

  • Tell you how to calculate false positives given the prevalence of the disease and the specificity of the diagnostic test; and

  • Discuss the notion of false positive rate and explain how to calculate it based on either specificity or on the number of false positives and true negatives.

What are the false positive cases?

False positives are healthy people who obtained a positive result in a diagnostic test, i.e., who were incorrectly identified as sick. It is one of the four possible combinations of test outcome and real patient status, as summarized in the following table.

Sick

Healthy

Positive test

True positive

False positive

Negative test

False negative

True negative

TotalSick

TotalHealthy

How do I calculate false positives?

The percentage of false positives (i.e., of healthy people with a positive test result) can be computed from specificity and prevalence via the following equation:

False positives = (100% - Specificity) × (100% - Prevalence)

🙋 Recall that:

  • Prevalence of a disease is the probability of this disease in the entire population.

  • Specificity of a test is the probability of a healthy person getting a negative result. In other words, it's the true negative rate. This is a complementary notion to the false positive rate.

How do I calculate true negatives?

True negatives are people who are healthy and obtained a negative test result. That is, their status as non-disease was correctly identified by the diagnostic test. Calculating true negatives is similar to calculating false positives:

True negatives = Specificity × (100% - Prevalence)

What is the false positive rate?

The false positive rate is the proportion of false positives to the total number of healthy people (regardless of whether their test status was correct – true negatives; or incorrect – false positives). In other words, the false positive rate is the probability of the test yielding a positive result incorrectly, i.e., in a healthy patient.

How do I calculate the false positive rate?

The false positive rate can be computed from the number of false positive and true negative cases as:

False positive rate = 100% × False positives / (False positives + True negatives).

Alternatively, the false positive rate can be computed from specificity by:

False positive rate = 100% - Specificity.

If you want to learn more about assessing the accuracy of diagnostic tests, you'll benefit from visiting the following tools:

FAQ

What is the false positive rate if the specificity is 93%?

The false positive rate is 7%. The calculation of the false positive rate given specificity is very straightforward:

False positive rate = 100% - Specificity

In our example:

False positive rate = 100% - 93% = 7%.

What is the false positive rate if the prevalence is 5%?

The false positive rate cannot be calculated based on the prevalence alone! You need the specificity or the number of false positives and true negatives.

Anna Szczepanek, PhD
Prevalence
%
Specificity
%
False positive
%
True negative
%
False positive rate
%
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