# Significance of regression coefficients and interpretation problems

#### pff

##### New Member
Dear All,
I am currently facing a problem regarding the statistical interpretation of nonsignificant coefficients. I would like to know whether there might be a valid statistical explanation for a coefficient not being significant.

So, my questions is the following: how can I statistically justify that the coefficients are not significant?
In my case I have a dummy indipendent variable (coded 0/1) which shows a p-value higher than the significance level chosen.
Might it because the number observations coded 1 for that specific explanatory variable are not many in the sample? Is there any other explanation attributable to the structure of the sample maybe?
or is it something else that I have to consider?

I would be grateful if you could help me and give me some suggestions.
Thank you

#### krytellan

##### New Member
Of course, there could be a statistical reason why there was no significance. It is just as likely that there is no significance because what you expected to find is not there.

#### pff

##### New Member
Yes sure, you can find attached in the word file the charts for the dependent variable and the results of the GLM I run below them.
I have considered the proportion of Chinese banks in a group of banks financing loans in different sectors. The sectors are four and I have inserted a dummy for 3 of them.
The problem is that for one of these sectors (Natural resources) the coefficient is not significant, but it is also true that the number of observations for this sector is not that high. Does it have any effect?
What do you think I can say on this?

Besides this is a GLM with logit link and binomial family so the interpretation is slightly different from the linear regression right?

Thanks a lot

#### Mean Joe

##### TS Contributor
You could say that it is not showing significance because the sample size is too small; but then you can almost always say that. With a large enough sample size every little difference can be statistically significant.

Looking at the coefficient, it is not really that big, so it is not so significant. I believe the p-value is derived from the statistic (chi-square distribution) which equals (coefficient/standard error)^2. Or maybe it's not squared. But basically, when you have a larger sample size then standard error decreases, so that statistic becomes larger, and hence p-value becomes smaller.