False positives and false negatives

When testing for the presence of a disease, the results obtained are often not 100% reliable. In this article we explain false positives and false negatives in test results. The graphics are dynamic, if you change the input numbers, then they'll update.
Let's start with the prevalence of disease, this is the proportion of positive cases in the population.
Disease prevalence input: %


Light red shows the proportion of the population that have the disease, i.e. are positive.
Light blue shows the proportion of the population that don't have the disease, i.e. are negative.


The false negative rate is the proportion of the positive cases that are incorrectly deemed to be negative.
False negative input: %


Dull red shows the true positives: the proportion of the population that are positive and get positive test results.
Orange shows the false negatives: the population that are positive but get negative test results.


The false positive rate is the proportion of the negative cases that are incorrectly deemed to be positive.
False positive input: %


Yellow shows the false positives: the population that are negative but get positive test results.
Dull blue shows the true negatives: the proportion of the population that are negative and get negative test results.


One challenge when considering an individual positive test result is that it is not clear whether it is a true positive or a false positive. We can look at the likelihood of each:

Dull red shows the true positives: the proportion of the population that are positive and get positive test results.
Yellow shows the false positives: the population that are negative but get positive test results.

Using the values that were input above for prevalence, false positives and false negative,
we find that of the positives:

True positives:
False positives:

When the prevalence is low, it is common to have a situation where there are more false positives than true positives. You can try this out for yourself by reducing the prevalence number above.