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Re: st: Why F-test with regression output

From   Richard Williams <>
Subject   Re: st: Why F-test with regression output
Date   Wed, 04 May 2011 23:15:00 -0500

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.


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
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