Closed testing procedure

In statistics, the closed testing procedure[1] is a general method for performing more than one hypothesis test simultaneously.

The closed testing principle

Suppose there are k hypotheses H1,..., Hk to be tested and the overall type I error rate is α. The closed testing principle allows the rejection of any one of these elementary hypotheses, say Hi, if all possible intersection hypotheses involving Hi can be rejected by using valid local level α tests. It controls the familywise error rate for all the k hypotheses at level α in the strong sense.

Example

Suppose there are three hypotheses H1,H2, and H3 to be tested and the overall type I error rate is 0.05. Then H1 can be rejected at level α if H1 ∩ H2 ∩ H3, H1 ∩ H2, H1 ∩ H3 and H1 can all be rejected using valid tests with level 0.05.

Special cases

The Holm–Bonferroni method is a special case of a closed test procedure for which each intersection null hypothesis is tested using the simple Bonferroni test. As such, it controls the familywise error rate for all the k hypotheses at level α in the strong sense.

Multiple test procedures developed using the graphical approach for constructing and illustrating multiple test procedures[2] are a subclass of closed testing procedures.

gollark: Now to waste another 3 or so diamonds on moar tracks.
gollark: Maybe I can "fix" it by adding an extra `sleep` at the end or something.
gollark: My code waits `((length / 6000) / speed) - 2` seconds, then inefficiently checks the position of the tape every 0.05 seconds to see if it's hit the end.
gollark: I found that it reads 6000 bytes a second.
gollark: I'm not sure if it's that they're written to the tapes that way, or whether my code for determining the end of a track is a bit broken.

See also

References
  1. Marcus, R; Peritz, E; Gabriel, KR (1976). "On closed testing procedures with special reference to ordered analysis of variance". Biometrika. 63: 655–660. doi:10.1093/biomet/63.3.655. JSTOR 2335748.
  2. Bretz, F; Maurer, W; Brannath, W; Posch, M (2009). "A graphical approach to sequentially rejective multiple test procedures". Stat Med. 28 (4): 586–604. doi:10.1002/sim.3495.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.