Precision of the point estimate and SE

[Neelakanda Krishna]

Dear Stata members
I would like get some basic idea on what do you mean by precision of the point estimate in reference to its Standard error and t stat. Please follow the below regression result for the illustration purposes

           |               Robust
       lever_w | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
        
  
               
        size_w |  -.0060164   .0098228    -0.61   0.540    -.0253001    .0132674
     cash_ta_w |   .0750381   .0684868     1.10   0.274    -.0594125    .2094888
          pb_w |  -.0008145   .0017106    -0.48   0.634    -.0041727    .0025437
           age |  -.0168279   .0321798    -0.52   0.601    -.0800021    .0463463
--------------------------------------------------------------------------------

Based on the conventional p-value based decision, none of the variables are "statistically significant" (I know that is not a good usage but for the ease of exposition). But point estimates are of different magnitude and in this context, say age has coefficient of .016 with bigger SE of .032 while cash has a point estimate of .0750 with a less standard error. For pb_w, the coefficient is very less but standard error is also small.

In this context I would like to ask if one has to explain these 4 variables, which one is more precise among the 4 and for which variable we can surely rule out any association on dependent variable. In terms of describing the results in these context, where would one has to focus first, point estimate or SE or CI.

Some references that helped to me to have this query

Thus, unless the point estimate (observed association) equals the null value exactly, it is a mistake to conclude from P > 0.05 that a study found “no association” or “no evidence” of an effect
Source: Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877414/

What does here "null value" mean? If that is 0 implied, then in my above table only for pb_w, it applies, right? If so, can I say that pb_w has no association with dependent var with certainty.

Standard errors are large or small relative to the coefficients, and also relative to the goals of your research. Let's say, for the sake of an example, that the coefficient of z is 1.5. Then relative to that coefficient, the standard error of 0.057865 is pretty small, and for most purposes you can probably rest easy. But if the nature of your research goal is such that you need an estimate of z that is precise to within 0.001, then that standard error is an order of magnitude too large. So it really boils down to a practical question: how precise does your estimate of the coefficient need to be?
Source: Clyde Schechter https://www.statalist.org/forums/for...08#post1348108

In Clyde's example the point estimate is Statistically Significant as t stat is 1.5/.057865=26. Now when standard error is say .001, the t-stat will be 1500 and do we need up to that value to clearly say an association.

I have a referred a few textbooks but they are not very much clear in this and if someone could take me through this, that will strengthen my understanding

[Carlo Lazzaro]

Neelakanda:
probably point #23, page 344 of the article you mentioned offers the best reply to your main question.

[Neelakanda Krishna]

Dear Carlo Lazzaro
Thanks for the swift reply. Yes, they have mentioned "When the model is correct, precision of statistical estimation is measured directly by confidence interval width (measured on the appropriate scale). It is not a matter of inclusion or exclusion of the null or any other value

[Carlo Lazzaro]

Exactly.