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Re: st: Fw: Multiple One-Tailed Tests


From   Roger Newson <r.newson@imperial.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Fw: Multiple One-Tailed Tests
Date   Thu, 8 Jul 2010 11:11:43 +0100

No, adding more regressors does not alter the number of comparisons, because the number of comparisons is still 2, so we still use 100(1-alpha/2)% confidence intervals, and a rectangular Cartesian product confidence interval.

However, if we wanted a joint conservative confidence region for the 3 parameters b1, b2 and b3, then we would need to calculate a 100(1-alpha/3) confidence interval for each of the 3 parameters. The Cartesian product of these confidence intervals will then be a 3-dimensional Bonferroni-corrected confidence interval for the parameter (b1,b2,b3).

The main problem here is that (for whatever reason) the -level()- parameter of -regress- cannot take values with more than 2 decimal places. For alpha=0.05, 100*(1-alpha/3) is (approximately) 98.333333. A possible answer is to use the -parmest- package, downloadable from SSC (for Stata 11 users) or from my website (for users of earlier Stata versions). You might then type, in the -auto- data,

regress mpg weight length price
parmest, level(`=100*(1-0.05/3)') list(, abbr(32))

and view 98.33333333333% confidence intervals for the parameters. The -parmest- package can also be used in this way to produce Sidak-corrected confidence intervals, which are slightly less conservative than Bonferroni-corrected confidence intervals.

I hope this helps.

Best wishes

Roger


Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 08/07/2010 04:51, Bea Potter wrote:
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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