Interpreting the alpha level of coefficients

[Karlie Krebs]

Hi Statalist,

How would I know the significance level of a variable based on its coefficient and standard error? For example, Stata gives me a coefficient of 0.26 and a standard error of 0.013. How would I calculate this or know that it is significant at p<0.001? I realize that Stata also outputs the p-value for me, but I would like to know how to tell the alpha level when it is not given to me (ie., in a table).

Thanks.

[Carlo Lazzaro]

Karlie:
it is easy to get what you're after:

use auto.dta, clear
reg price mpg
ereturn list
di 11253.06/1170.813
di 2*ttail(e(df_r),9.61)

A smarter approach would call for retrieving alpha coefficient and standard error directly from the matrices that Stata uses in performing -regress- (please see -help matrix_utility- and related entries in Stata 13.1 .pdf manual).

[Karlie Krebs]

Thanks, Carlo. This was very helpful. How would I do this manually or without Stata? For example, if I was looking at a regression table and the only information I have is a coefficient and standard error?

[Carlo Lazzaro]

Karlie:
provided that the critical alpha is set at 0.05, you need two more pieces of information: the distribution of your coefficient and the degrees of freedom of your model.
Let's assume that you're dealing with a linear regression model and that the constant you get in the regression output is 0.26, with a standard error of 0.013 (as you reported in your previous post).
Now:
- let's calculate the t: 0.26/0.013=20.
Without knowing how many degrees of freedom you have to consider, it is impossible to state whether t=20 indicates that, should you re-run the same regression model on a sample of the same size n times the probability of obtaining by chance a value as extreme as the one reported in the output of you regression for the constant is negligible (that is, <0.05).
Hence, let'assume that, as implicitly reported in the example embedded in my previous post, the degrees of freedom are 72.
Reading across the statistical table of the t-distribution (available as appendix in any decent basic statistics textbook), you will find the one-side p-value for each combination of t and degrees of freedom. You if you're loking for a two-side p-value, you can get it by simply taking two times the one-side p-value you have found in the statistical table of the t-distribution.
As an aside, after 120 degrees of freedom, the t-distribution is replaced by the z-distribution.
According to the aforementioned example, t=20 with 72 degrees of freedom means that the constant of your regression model is highly statistically significant (p=0.000).

[Maarten Buis]

Also see: http://www.stata-journal.com/article...article=st0137

[Carlo Lazzaro]

Karlie:
Maarten's interesting article is exactly about the smarter approach I mentioned in post #2!