Hello Zoya, I prefer to use research questions, and test them; rather than hypotheses.  Then I still report the results of statistical tests including F, its p-value , Z or t, and the 2 tailed p-value of the t test.

can you please share the ban notification with me Its  not know to many here

The ban was unfortunate and based on misconceptions. It is OK to use statistical tests but it is of course not OK to make incorrect and inflated interpretations of the results of such tests. 

Hello Subrata, you can find that editorial article from Basic and Applied Social Psychology with the ban here http://www.tandfonline.com/doi/abs/10.1080/01973533.2015.1012991.

About this ban, I understand that it is caused by the fact that p-value and the concept of statistical significance has been widely misunderstood and misused by many non-statistician researchers. BASP is not the first journal that tries to deal with this problem, the journal Epidemiology also banned p-value in 1996 for some time. Some authors, like Cumming  or Sterne, suggest not to use word significant at all and also to concentrate on actual effect sizes and confidence intervals when interpreting results.

These bans really come from an incorrect use and application of some statistical methods. There is a lack of understanding with p-values and confidence intervals, that however does not make them useless or invalid. It means one should be careful in interpreting the results and consider what population is actually modeled in the results. I have not heard of life science journals banning them but I do not do much research in those fields.  I would be more than happy to collaborate and help make sure things were interpreted and analyzed correctly if that could help. (I am a Biostatistician)

Zoya -

As perhaps indicated by others, the problem is that p-values have been used as if they are more meaningful than they are.  An isolated p-value does not generally give you enough information to make a meaningful decision, but many journals have apparently been run as if one would.  So a ban is a reaction against that.  It seems like perhaps a rather strong reaction, but I am glad to see this issue has finally gotten the attention it deserves, though i am not completely certain that this was the best way to do it.  However, this problem has been going on for a long time:

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

I would be surprised to see many more such 'bans,' but then the one in effect was a surprise as well. 

You may also be interested in the following:

 https://www.researchgate.net/post/How_to_acknowledge_in_the_discussion_section_of_a_paper_that_a_hypothesized_relation_is_statistically_significant_but_not_practically_significant

Note that "effect size" is important. At a glance, the following looks like it might be somewhat helpful here:

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

You asked the following:

"Or is it OK to report results of statistical tests but just interpret them more carefully in regards of p-values?"   I'd say you have a reasonable approach (say, a p-value with a type II error probability, or say sequential testing that compares two 'simple' hypotheses), but you never know what a journal may decide to require or 'ban.'  You need to try to do something reasonable within the confines imposed upon you.

Best wishes - Jim

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

Standard deviations and standard errors are relatively straightforward to use and interpret, but hypothesis tests can be rather nebulous.  A lone p-value is fairly meaningless, and often misleading.  Here is a recent, but long overdue, press release from the American Statistical Association:

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