Re: st: Why F-test with regression output

[John Antonakis <John.Antonakis@unil.ch>]

Hi:

The F-test for all betas = 0 is useful only if it is theoretically 
useful; otherwise, it doesn't mean much. Suppose I want to estimate the 
effect of x on y and x is a "new kid" on the block--so, I stick in a 
whole bunch of controls. It is possible that the overall F-test is not 
significant because most of the controls don't do much. OK you'll say, 
but then they were not well selected; however, if the theory suggest 
that we must partial out the variance due to those controls and the 
coefficient of x is significant but the F-test is not, I think that 
these results are very meaningful.

I too think, as Joerg suggested, that the importance of the F-test is 
probably due to psychological experimental research, where one or two 
variables were exogenously manipulated, so the F-test there would 
indicate whether the experiment worked (though  again, it is possible 
that one controls for a competing treatment, or many competing 
treatments that are placebos that might not work and which might make 
the F-test non significant).

Best,
J.

__________________________________________

Prof. John Antonakis
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
The Leadership Quarterly
__________________________________________


On 05.05.2011 06:15, Richard Williams wrote:
> At 04:19 PM 5/4/2011, Steven Samuels wrote:
>
> > Nick, I've seen examples where every regression coefficient was 
> > non-significant (p>0.05), but the F-test rejected the hypothesis that 
> > all were zero. This can happen even when the predictors are 
> > uncorrelated. So I don't consider the test superfluous.
> >
> > Steve
>
> I also find the omnibus test helpful.
>
> If, say, there were a lot of p values of .06, it is probably very 
> likely that at least one effect is different from 0.
>
> If variables are highly correlated, the omnibus F may correctly tell 
> you that at least one effect differs from 0, even if you can't tell 
> for sure which one it is.
>
> In both of the above cases, if you just looked at P values for 
> individual coefficients, you might erroneously conclude that no 
> effects differ from zero when it is more likely that at least one 
> effect does.
>
> If the omnibus F isn't significant, there may not be much point in 
> looking at individual variables. If you have 20 variables in the 
> model, one may be significant at the .05 level just by chance alone, 
> but the omnibus F probably won't be. That is, a fishing expedition for 
> variables could lead to a few coefficients that are statistically 
> significant but the omnibus F isn't.
>
> Incidentally, you might just as easily ask why the Model Chi Square 
> gets reported in routines like logistic and ordinal regression. The 
> main advantage of Model Chi Square over omnibus F is that Model Chi 
> Square is easier to use when comparing constrained and unconstrained 
> models (e.g. if model 1 has x1 and x2, and model 2 has x1, x2, x3, and 
> x4, I can easily use the model chi-squares to test whether or not the 
> effects of x3 and/or x4 significantly differ from 0).
>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
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>
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