True/false positive/negative

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Create redirects for things like true positive and use the anchors below Alec (talk) 13:28, 14 December 2017 (UTC)

Definition

Suppose we have a situation [ilmath]A[/ilmath] which is boolean and thus can only take the values [ilmath]0[/ilmath] (situation [ilmath]A[/ilmath] is false) and [ilmath]1[/ilmath] (situation [ilmath]A[/ilmath] is true) and an interpretation [ilmath]B[/ilmath], with the intention of interpreting whether or not the situation is [ilmath]A[/ilmath] or not.

That is [ilmath]B\eq 1[/ilmath] indicates that the interpretation is that [ilmath]A[/ilmath] is happening, and [ilmath]B\eq 0[/ilmath] is that it is not.

Then, once [ilmath]A[/ilmath] is known we can classify the [ilmath](A,B)[/ilmath] tuple as follows:

1. [ilmath]A\eq 0[/ilmath] and [ilmath]B\eq 0[/ilmath]: true negative, [ilmath]B[/ilmath] has correctly (truely) indicated a negative ([ilmath]A[/ilmath] is not happening) result
2. [ilmath]A\eq 0[/ilmath] and [ilmath]B\eq 1[/ilmath]: false positive, [ilmath]B[/ilmath] has indicated a positive result, falsely, as in actuality it's negative
3. [ilmath]A\eq 1[/ilmath] and [ilmath]B\eq 0[/ilmath]: false negative, [ilmath]B[/ilmath] has indicated a negative result, falsely, as in actuality it's positive
4. [ilmath]A\eq 1[/ilmath] and [ilmath]B\eq 1[/ilmath]: true positive, [ilmath]B[/ilmath] has correctly indicated a positive result.

The positive/negative part refers to the interpretation and it's true if the situation was correctly predicted by the interpretation ([ilmath]A\eq B[/ilmath]), otherwise it's false.

This terminology is used in instances of statistical tests

Specific definitions

True Negative

The interpretation of being negative matches the situation.

False Positive

The interpretation was positive, suggesting the situation was happening, however in reality situation was not happening, and this situation was wrongly classified as positive.

False Negative

The interpretation was negative, suggesting the situation wasn't happening, however in reality the situation was happening and was wrongly classified as not happening.

True Positive

The interpretation correctly identified the situation as "happening" by indicating (correctly) a positive result.