False positive rate

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 is calculated as the ratio between the number of negative events wrongly categorized as positive (false positives) and the total number of actual negative events (regardless of classification).

The false positive rate (or "false alarm rate") usually refers to the expectancy of the false positive ratio.

The false positive rate is ${\displaystyle {\frac {FP}{N}}={\frac {FP}{FP+TN}}}$,

where FP is the number of false positives, TN is the number of true negatives and N=FP+TN is the total number of negatives.

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 ${\displaystyle V/m_{0}}$.

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