When trying to identify dangerous offenders (or other things as well), researchers often make mistakes. One of these mistakes is known as a false positive. The false positives error is identifying someone as dangerous (and possibly keeping them incarcerated or denying them parole) when they are not dangerous.

The opposite of false positives would be a false negative: identifying someone as non-dangerous when they in fact go on to commit a dangerous act.

**Bayes' theorem**

The probability that an observed positive result is a false positive (as contrasted with
an observed positive result being a true positive) may be calculated using Bayes' theorem.

The key concept of Bayes' theorem is that the true rates of false positives and false negatives are not a function of the accuracy of the test alone, but also the actual rate or frequency of occurrence within the test population; and, often, the more powerful issue is the actual rates of the condition within the sample being tested.

Type I errors and Type II errors are very often referred to as false positives and false negatives respectively. The terms are now commonly applied in much wider and far more general sense than Neyman and Pearson's original specific usage, as follows:

Type I errors (the false positive): the error of rejecting something that should have been accepted; an expamle of false positives is finding an innocent person guilty.

Type II errors (the false negative): the error of accepting something that should have been rejected; an expamle of false negative is finding a guilty person innocent.

We also have true positive, false positive, true negative, false negative.

**False positives in Spam
filtering**

While most anti-spam tactics can block or filter a high percentage of unwanted emails,
doing so without creating significant false-positive results is a much more demanding
task. A false negative occurs when a spam email is not detected as spam, but is classified
as "non-spam".