FWER Definition
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 Hi 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 |
- is the number of true null hypotheses, an unknown parameter
- is the number of true alternative hypotheses
- is the number of false positives (Type I error)
- is the number of true positives
- is the number of false negatives (Type II error)
- is the number of true negatives
- is the number of rejected null hypotheses
- is an observable random variable, while, and are unobservable random variables.
The FWER is the probability of making even one type I error In the family,
or equivalently,
Thus, by assuring, the probability of making even one type I error in the family is controlled at level .
A procedure controls the FWER in the weak sense if the FWER control at level is guaranteed only when all null hypotheses are true (i.e. when = so the global null hypothesis is true)
A procedure controls the FWER in the strong sense if the FWER control at level is guaranteed for any configuration of true and non-true null hypotheses (including the global null hypothesis)
Read more about this topic: Familywise Error Rate
Famous quotes containing the word definition:
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)