A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition when the condition is not present. False positives can occur in various fields, including medical screening, scientific research, and cybersecurity. For example, in medical screening, a false positive can occur when a test result indicates the presence of a disease when the patient is actually healthy. False positives can be costly, as they can lead to unnecessary follow-up testing and treatment.

It is important to distinguish between the type 1 error rate and the probability of a positive result being false. A false positive error is a type 1 error where the test is checking a single condition and wrongly gives a positive decision. False positives can also produce serious and counter-intuitive problems when the condition being searched for is rare, as in screening.

In contrast, a false negative is a test result that wrongly indicates that a condition does not hold. For example, a pregnancy test that indicates a woman is not pregnant when she is, or when a person guilty of a crime is acquitted, these are false negatives. False negatives can be equally harmful, especially when the condition being searched for is common.

False positives and false negatives are important concepts in machine learning, where they are used to evaluate the performance of classification models. A true positive is an outcome where the model correctly predicts the positive class, while a true negative is an outcome where the model correctly predicts the negative class. A false positive is an outcome where the model incorrectly predicts the positive class, while a false negative is an outcome where the model incorrectly predicts the negative class.