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
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Madan Gopal Kundu
Biostatistician I, i3 Statprobe
Gurgaon, Haryana
India
Web: http://www.freewebs.com/madanstata
mobile: 91-9868788406
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