False positives and false negatives

Diagram of a binary classifier separating a set of samples into positive and negative values.

The elements in the green area on the right are those classified as positive matches for the tested condition, while those on the pink area on the left were classified as negative matches.The red crosses () within the green area () represent false positives (negative samples that were classified as positive).Conversely, the green circles () within the pink area () represent false negatives (positive samples that were classified as negative).A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result incorrectly indicates the absence of a condition when it is actually present.

However it is important to distinguish between the type 1 error rate and the probability of a positive result being false.

For example, when a pregnancy test indicates a woman is not pregnant, but she is, or when a person guilty of a crime is acquitted, these are false negatives.

The hazards of reliance on p-values was emphasized in Colquhoun (2017)[2] by pointing out that even an observation of p = 0.001 was not necessarily strong evidence against the null hypothesis.

As a consequence, it has been recommended[2][6] that every p-value should be accompanied by the prior probability of there being a real effect that it would be necessary to assume in order to achieve a false positive risk of 5%.

The article "Receiver operating characteristic" discusses parameters in statistical signal processing based on ratios of errors of various types.