出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/08/22 03:26:15」(JST)
In statistics, when performing multiple comparisons, the term false positive ratio, also known as the false alarm ratio, usually refers to the probability of falsely rejecting the null hypothesis for a particular test.
The false positive rate (or "false alarm rate") usually refers to the expectancy of the false positive ratio.
The false positive rate is .
Where FP is number of false positives, and TN is number of true negatives.
Suppose we have m null hypotheses, denoted by: H1, H2, ..., Hm.
Using a statistical test, each hypothesis is declared significant/non-significant.
Summing the test results over will give us the following table and related random variables:
| Null hypothesis is True | Alternative hypothesis is True | Total | |
|---|---|---|---|
| Declared significant | |||
| Declared non-significant | |||
| Total |
The level of significance that is used to test each hypothesis is set based on the form of inference (simultaneous inference vs. selective inference) and its supporting criteria (for example FWER or FDR), that were pre-determined by the researcher.
When performing multiple comparisons in a statistical framework such as above, the false positive ratio (also known as the false alarm ratio, as opposed to false positive rate / false alarm rate ) usually refers to the probability of falsely rejecting the null hypothesis for a particular test. Using the terminology suggested here, it is simply .
Since V is a random variable and m_0 is a constant (), the false positive ratio is also a random variable, ranging between 0-1.
The false positive rate (or "false alarm rate") usually refers to the expectancy of the false positive ratio, expressed by .
It is worth noticing that the two definitions ("false positive ratio" / "false positive rate") are somewhat interchangeable. For example, in the referenced article[1] serves as the false positive "rate" rather than as its "ratio".
| This section possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (February 2013) |
While the false positive rate is mathematically equal to the type I error rate, it is viewed as a separate term for the following reasons:[citation needed]
The false positive rate should also not be confused with the familywise error rate, which is defined as . As the number of tests grows, the familywise error rate usually converges to 1 while the false positive rate remains fixed.
Lastly, it is important to note the profound difference between the false positive rate and the false discovery rate: while the first is defined as , the second is defined as .
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| リンク元 | 「偽陽性率」 |
| 拡張検索 | 「false-positive rate」 |
| 関連記事 | 「rate」「rat」「positive」「false」「False」 |