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Re: st: T-test and F-test


From   Roger Newson <r.newson@imperial.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: T-test and F-test
Date   Mon, 5 Jul 2010 14:51:00 +0100

In general, a high P-value (as Natasha has with the t-tests) does NOT prove a null hypothesis of a zero difference. It only implies that the confidence interval for the difference contains a zero difference, and also contains a range of small positive or negative non-zero differences.

And, in the case of an F-test on the joint effects of x and z, the P-value corresponds to an elliptical confidence region of possible x-effects and z-effects, in a 2-dimensional space of bivariate parameter values (beta_x,beta_z), representing possible combinations of an x-efffect and a z-effect. In Natasha's case, this elliptical confidence region does not contain the value (0,0), implying that both effects are zero. However, the confidence region probably does extend across both axes, and therefore does contain bivariate parameter values (beta_x,beta_z) in which the beta_x is zero and beta_z is non-zero, and also contains bivariate parameter values (beta_x,beta_z) in which the beta_z is zero and the beta_x is nonzero.

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 05/07/2010 13:57, natasha agarwal wrote:
On Mon, Jul 5, 2010 at 12:42 PM, Roger Newson<r.newson@imperial.ac.uk>  wrote:
Yes. The data may be compatible with the possibility that the first
difference is zero, and compatible with the possibility that the second
difference is zero, but not compatible with the possibility that BOTH
differences are zero. So, at least one of the differences seems to be
non-zero, but the data are insufficient to be sure which one is non-zero, or
to be sure that BOTH are nonzero.

So supposing I estimate a model reg y x z

now the t-stats on x and z are insignificant but when I perform a F
test, they both are jointly significant. So are you trying to say that
  because the data is unsure which one is non-zero (which I find it
confusing since the t-stats both reveal that they are insignificant)
or to be sure that Both are nonzero and hence the F might be
significant while t can be insignificant?

Thanks
Natasha


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 05/07/2010 12:36, natasha agarwal wrote:

Dear everyone,

Can anyone explain me why the t-test statistics for variables in the
model are statistically insignificant but when tested for joint
significance (F-test) they are jointly significant?

Thanks
Natasha
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