interpretation of non significant coefficients

[mian rafay]

Dear All,
I am currently facing a problem regarding the statistical interpretation of non significant 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 independent 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?

could i explain any relationship on the basis of signs of coefficients.

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

[Nick Cox]

I am not sure that your question allows anything than obvious comments. There is absolutely no information on what you did and your precise results.

Significance is like reputation: some predictors have higher values than they deserve; with others it is the other way round; with yet others it's probably about right, except there is no Olympian standpoint from which correct values can be seen.

A non-significant coefficient is often helpful: it may suggest a way to simplify an over-complicated model and it may indicate what doesn't make sense. In many fields, there are numerous vague, arm-waving suggestions about influences that just don't stand up to empirical test.

What I find all too often is that people think that the table of results will, or should, in some sense tell them why they get those results and what they mean.

What I find all too often neglected:

1. Generally, plotting the data to check apparently weak relationships. Added variable plots are good for standard regression models.

2. Specifically, plotting predictors against other predictors. Often a bundle of predictors is competing with each other for a small market share.

[mian rafay]

thanks for your reply
i am just looking for interpretation if any.for my regression where i have dummy variable with as expected sign of coefficient but non significant.

[Carlo Lazzaro]

Myan:
I do share Nick's comments; I like especially his first point: how can others help you out if you do not help them help you out by posting what youn typed and what Stata gave you back (as per FAQ)?
I would only add that (assuming that a real difference exists in what you are comparing), the most trivial reason why your coefficients "let you down" (although a non-significant coefficient is as decent as a significant one) is that your sample is too small. Hence, if that were the case,go out and collect other data may be a (often unfeasible, though) good first recipe.

PS: crossed in the cyberspace with Mian's second post, that does not seem to adress Nick's wise first point.

[Nick Cox]

Here is a crude first model. I agree with anyone offended by the use of algebra here, but I want to make a point strongly.

Interpretation = substantive thinking about model + statistical thinking about model + statistical thinking about dataset + substantive thinking about dataset + statistical thinking about results.

Two of those terms can usually only be supplied by researchers in the same field. All of these are hard to teach; the practice of any can not be conveyed well by preaching or pontification.

Also, sometimes the data tell you that you (the researcher, the group of researchers, the discipline) are wrong. They hint that rather than shout it, but the attitude that the idea is right but the results must be at fault for not showing it clearly is a bad one to follow.

To put it differently, your question is close to the limiting form: Some of my results I find puzzling. How do I explain that? I understand that the question is common, but it's difficult to answer usefully.

[Richard Williams]

There are so many possible explanations for an insignificant effect. Maybe the effect really is zero. Maybe your sample size is too small to detect a non-zero effect. Maybe there are measurement problems, e.g. the measures are unreliable or don't validly measure the concepts you are interested in. Maybe the effect of a variable is indirect rather than direct, e.g. A-->B-->C, and once B is included in the model for C the estimated effect of A is zero. Perhaps the sample is not representative of the larger population hence leading to inaccurate conclusions. If you think an insignificant effect is implausible (e.g. it goes counter to existing research) you may want to consider whether possibilities like I have just suggested should be considered further.