Standard error logic Obviously the closer the standard error to zero the better. However, what if the values the in which the standard errors are from are extremely large and the standard errors are much higher than zero but proportionately small.
For example:
What if you have a model with a slope coefficient of 0.5 and the standard error was 0.05 and another model with a slope coefficient of 1000 and a standard error of 10.
Would the latter be considered a better standard error?

This could be where the p-value comes in.
In the first case, the estimated parameter is $10$ standard errors away from zero. This will result in a small p-value.
In the second case, the estimated parameter is $100$ standard errors away from zero. This will result in an even smaller p-value.
To some extent, this depends on the sample size (at least for t-stats, but not for z-stats), though that should not be much of an issue for so dramatic of a difference as $10$ and $100$.
