Re: st: Why F-test with regression output

[Richard Williams <richardwilliams.ndu@gmail.com>]

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).


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Richard Williams, Notre Dame Dept of Sociology
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