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very true ; see the notion of "effect size"

https://en.wikipedia.org/wiki/Effect_size

(and the comment about the misuse of p-values)

if you are concerned by the smallness of the effect size with very large samples, you could just avoid testing against an equality null hypothesis ; you could test for a minimum difference between the samples, hence controlling directly the"pragmatically relevant difference" between samples (regardless the size of the samples) instead of probing the "statistically significant difference" (sample-size dependent as with an equality null hypothesis)

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That is a very good question. 

What comes to my mind is this: Go for literature review and see if effect sizes correspond with your results. 

Well it is true that increasing sample sizes you increase a chance do detect significant associations. However, with underpowered studies you are facing the possibility of Type II errors to occur.

Regards, Witold

Hassan -

It has long been a problem that p-values have been misunderstood and overused.   An isolated p-value is nearly meaningless.   See my explanation of interpretation of hypothesis testing here:

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

The American Statistical Association (ASA) has finally - way overdue - taken a stand on this.  Here is a recent press release:

 http://www.amstat.org/newsroom/pressreleases/P-ValueStatement.pdf

The basic fact is that a p-value is a function of sample size, like a standard error of a mean used in a confidence interval.  But a confidence interval - or in regression, a prediction interval - gives you two end-bounds for a given level.  A p-value is misleading because it only gives you one measure that leads people to make decisions that may be based on sample size alone. With a small enough sample size, you cannot 'disprove' anything.  With a large enough sample size, nothing seems possible to be 'proven.'  Thus effect size is important, as Fabrice indicated, and I think such considerations are often handled best by considering probabilities of type II errors, as noted by Witold. 

Regarding effect size, this looks like it might be interesting for you:

 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/

At any rate, i have often found that there are two sources which generally provide good information on statistics, online: (1) NIH (US National Institutes of Health), and (2) PSU (Pennsylvania State University).  There are many other good sources, but these seem to be generally good, rather consistently.

Cheers -

Jim 

PS  -   Andrew Gelman has an interesting note here, especially  regarding large sample sizes:

 http://andrewgelman.com/2009/06/18/the_sample_size/

Article Practical Interpretation of Hypothesis Tests - letter to the...

Dear Hassan

Your question include " infinite sample size" , I think in the real situation we have large, medium and small sample sizes with relative meaning to population.

The population can be finite or infinite, in large sample the effect size must be small and the power of the test must be high to have suitable results.

Good Luck