Significance (or p values) is a function of sample size. The larger the sample size, the more significant your p values.

In this context power is also an important modifier. Sometimes you do not have enough power to detect a significant effect, and sometimes on the contrary you have too much power to detect a very small effect. So in order to evaluate if that effect size is accurately estimated you should have an understanding of the amount of power you have.

Narrower confidence intervals are preferred. I can accept a borderline significant effect if it has a narrow CI and there is enough power to detect it. Wide confidence intervals need to be treated with caution.

Dear Chalamalla, thanks for the links.

Dear Sinan, thanks for your opinion. However, I need your insight. If a post-hoc power analysis indicates 46.4% for an OR of 1.81 [95% CI 0.64 - 5.10] , then what would be your interpretation? Would you say that the insignificance regarding the trend of increase in risk might be because of the inadequate power and this effect might get significant if a setting with adequate power is provided. In short, would you consider it as a signal or not?

How did you calculate post-hoc power? What is the sample size and other terms in the model? The power seems low, one could get a significant effect if enough power is used.

This is a question for a meta-analysis indeed. I just used the power calculator on web. Exposed events/total 7/1402, control events/total 11/5094.  

It seems you have enough sample size/power. Is this a result from a logistic regression model? Or the result of a case-control study or similar? What I want to learn is that if this is a crude or an adjusted odds ratio ? And I am still curious about the post-hoc power calculation. Can you send the link?

I'll send you an e-mail.

Hi Cem, 

Just one point: A post-hoc power analysis as presented ( a 46% power for an OR....) is  - excuse me the expression - statistical nonsense and cannot be subject to a meaningful analysis. It adds absolutely zero information, and, in fact, post-hoc power analysis should be a no-go in practically any imaginable scenario.

A good discussion by Russel Lenth is attached.

As for interpretation of point estimates and CIs, I suggest that you look to Philip Sedgwicks short BMJ statistical endgames for a starting point (a few links below) .All of his statistical 1-2 page pamphlets in BMJ are little short of brilliant

Best

Per

https://stat.uiowa.edu/sites/stat.uiowa.edu/files/techrep/tr378.pdf

http://www.bmj.com/content/349/bmj.g6051

http://www.bmj.com/content/350/bmj.h1113

http://www.bmj.com/content/345/bmj.e4960

http://www.bmj.com/content/344/bmj.e3147

Hi Per, many thanks for the answer and links.

Thank you Jochen. Every number has to be interpreted in the study's own context considering many details and there's no shortcut to the interpretation as far as I understood. 

Effect sizes and confidence intervals are in fact two very distinct things:

- Effect size is the result. If you are asked to summarize your finding using a single number, report the effect size.

- Confidence intervals is the precision. If you are asked: How reliable is the result, answer with the confidence interval. The wider the confidence interval is, the less precise is your result.

Thank you Denis. My aim in asking this question was to learn whether there are practical considerations. E.g. are there any thresholds for the interpretation?