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Subject:

Test of multiple hypotheses

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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]        Click to join Statisticians_group         ---------------------------------  Get the freedom to save as many mails as you wish. Click here to know how.```