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ALLSTAT  July 2007

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Subject:

Test of multiple hypotheses

From:

Madan Kundu <[log in to unmask]>

Reply-To:

Madan Kundu <[log in to unmask]>

Date:

Sat, 14 Jul 2007 08:32:15 +0100

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Hi Members,
   
  Hope you all are doing great. I had query related to testing of multiple hypotheses. I am describing it below:
   
  Consider three pair (null and alternate) of hypotheses:
  Pair - 1. Ho1 vs Ha1 (level of significance= alpha1)
  Pair - 2. Ho2 vs Ha2 (level of significance= alpha2)
  Pair - 3. Ho3 vs Ha3 (level of significance= alpha3)
   
  Now following cases arises:
   
  Case I:
   We want to test- 
  Ho: at least one of Ho1, Ho2 and Ho3 is true
  Ha: All three of Ha1, Ha2 and Ha3 are true
  Then our test strategy will be to test all of pair - 1, 2 and 3 and if in each case we reject null hupotheses then we will reject Ha in case I and in that case level of significance will be max(alpha1, alpha2, alpha3). This is simply the case of Intersection- Union test.
   
  Case II:
  We want to test- 
  Ho: All of Ho1, Ho2 and Ho3 are true
  Ha: At least one of Ha1, Ha2 and Ha3 is true
  Then our test strategy will be to test all of pair - 1, 2 and 3 and if in each case we reject null hupotheses then we will reject Ha in case I and in that case level of significance will be 1 - (1 - alpha1)*(1 - alpha2)*(1 - alpha3)
   
  Case III:
  We want to test
  Ho: At least two of Ho1, Ho2 and Ho3 are true
  Ha: At least two of Ha1, Ha2 and Ha3 are true
  In this case what will be our test strategy?? Can you suggest me some reference paper or online resources?
   
  Thanks & Regards
  Madan Kundu


          --------------
  

  Madan Gopal Kundu 
Biostatistician I, i3 Statprobe
  Gurgaon, Haryana
  India
  Web: http://www.freewebs.com/madanstata
  mobile: 91-9868788406
  e-mail: [log in to unmask] 
   





  
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