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FALSE POSITIVES

Sociologyindex, Sociology Books 2011, False Negative, False Positive

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 error is identifying someone as dangerous (and possibly keeping them incarcerated or denying them parole) when they are not dangerous. 

The other type of error 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; e.g., such as finding an innocent person guilty. 

Type II errors (the "false negative"): the error of accepting something that should have been rejected; e.g., such as finding a guilty person innocent. 

These examples illustrate the ambiguity of which is one of the dangers of this wider use: they assume the speaker is testing for innocence; they can also be used in reverse, as testing for guilt. The following table illustrates the conditions. Note that the terms true and false are used here in two different ways: the state of the actual condition (true/false); and the accuracy or inaccuracy of the test result (true positive, false positive, true negative, false negative).

Spam filtering
A false positive occurs when "spam filtering" or "spam blocking" techniques wrongly classify a legitimate email message as spam; and, as a result, interferes with its delivery. 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". A low number of false negatives is an indicator of the efficiency of "spam filtering" methods.

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