Re: st: T-test and F-test

[Roger Newson <r.newson@imperial.ac.uk>]

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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