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Re: st: Fw: Multiple One-Tailed Tests


From   Bea Potter <potterb80@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Fw: Multiple One-Tailed Tests
Date   Wed, 7 Jul 2010 20:51:31 -0700 (PDT)

Thank you all very much for the responses. 

I was hoping to ask a follow-up question when there are additional regressors

y = b0 + b1 x1 + b2 x2 + b3 x3 + u 

If we still want to test  whether we can reject b1>0 and b2<0, how does that 
change the test statistic? Or please let me know if there is a statistics 
reference that would be relevant. Thank you again. 




----- Original Message ----
From: "Airey, David C" <david.airey@Vanderbilt.Edu>
To: "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Sent: Wed, July 7, 2010 6:34:30 PM
Subject: Re: st: Fw: Multiple One-Tailed Tests

.

Because each coefficient is tested with the symmetric t distribution, we can 
make both of those alpha/2. And then their joint test, is what is wanted.

Thanks for clarifying that one, Roger and Maarten.


--- On Wed, 7/7/10, Bea Potter asked:
> > Given the following regression,
> > 
> > y = b0 + b1 x1 + b2 x2 + u 
> > 
> > we want to test whether we can reject b1>0 and
> > b2<0. 

--- On Wed, 7/7/10, Airey, David C answered:
> The joint test is the F statistic for the model, since b1
> and b2 are the only coefficients. So isn't it just alpha/2?

If I remember correctly the alpha/2 trick works because the
distribution of the test statistic (t distribution or normal
distribution) is symetric. This is not the case for the
F-distribution.

I had a look at this issue a while back, and it turned out 
not to be an easy problem. I'd love to be proven wrong 
though.

-- Maarten




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