Closed testing procedure: Difference between revisions

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==Example==
Suppose there are three hypotheses ''H''<sub>1</sub>,''H''<sub>2</sub>, and ''H''<sub>3</sub> to be tested and the overall type I error rate is 0.05. Then ''H''<sub>1</sub> can be rejected at level α if ''H''<sub>1</sub> ∩ ''H''<sub>2</sub> ∩ ''H''<sub>3</sub>, ''H''<sub>1</sub> ∩ ''H''<sub>2</sub>, ''H''<sub>1</sub> ∩ ''H''<sub>3</sub> and ''H''<sub>1</sub> can all be rejected using valid tests with level α = 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 [[familywisefamily-wise 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<ref>{{cite journal | doi = 10.1002/sim.3495 | last1 = Bretz | first1 = F | last2 = Maurer | first2 = W | last3 = Brannath | first3 = W | last4 = Posch | first4 = M | year = 2009 | title = A graphical approach to sequentially rejective multiple test procedures | journal = [[Stat Med]] | volume = 28 | issue = 4 | pages = 586–604 | s2cid = 12068118 }}</ref> are a subclass of closed testing procedures.
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{{Reflist}}
 
[[Category:Statistical hypothesis testing]]
[[Category:Statistical tests]]
[[Category:Multiple comparisons]]