Content deleted Content added
Citation bot (talk | contribs) Alter: pages. Add: s2cid, issue. Formatted dashes. | Use this bot. Report bugs. | Suggested by Smasongarrison | Linked from User:Smasongarrison/sandbox | #UCB_webform_linked 952/3850 |
Tadakichi2 (talk | contribs) m Changed the end of the example to use the value the example started with, instead of a letter |
||
| (4 intermediate revisions by 2 users not shown) | |||
Line 3:
==The closed testing principle==
Suppose there are ''k'' hypotheses ''H''<sub>1</sub>,..., ''H''<sub>''k''</sub> 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 ''H''<sub>''i''</sub>, if all possible intersection hypotheses involving ''H''<sub>''i''</sub> can be rejected by using valid local level α tests; the adjusted p-value is the largest among those hypotheses. It controls the [[
==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
==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 [[
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.
Line 21:
{{Reflist}}
[[Category:Multiple comparisons]]
| |||