In statistics, when performing multiple comparisons, a false positive ratio is 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 and the total number of actual negative events. The false positive rate usually refers to the expectancy of the false positive ratio'''.
Definition
The false positive rate is where is the number of false positives, is the number of true negatives and 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 and its supporting criteria, that were pre-determined by the researcher. When performing multiple comparisons in a statistical framework such as above, the false positive ratio 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 ' is a constant, the false positive ratio is also a random variable, ranging between 0-1.
The false positive rate usually refers to the expectancy of the false positive ratio''', expressed by. It is worthnoticing that the two definitions are somewhat interchangeable. For example, in the referenced article serves as the false positive "rate" rather than as its "ratio".
Classification of multiple hypothesis tests
Difference from "type I error rate" and other close terms
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:
The type Ierror rate is often associated with the a-priori setting of the significance level by the researcher: the significance level represents an acceptable error rate considering that all null hypotheses are true. the choice of a significance level may thus be somewhat arbitrary, 5%, 1%
Moreover, false positive rate is usually used regarding a medical test or diagnostic device, while type I error is a term associated with statistical tests, where the meaning of the word "positive" is not as clear.
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.
