There is a widespread notion that a p-value less than 0.05 is to be considered statistically significant, and above, not so.
I understand that the "0.05" was an arbitrary number, albeit arbitrated by a very smart man. In principle, it could've easily been 0.1, or 0.01. Most of the widespread support is just people using whatever everyone else is using.
This question asks, in effect IMO, whether it's okay to pick something like 0.07 as your threshold instead. Of course, probably it is preferable to select the threshold before you do your experiment, so that you don't end up in the silly situation where you results are significant because you happen to have picked your significance threshold to be whatever makes them significant.
But, once again, the 0.05 was arbitrary. It wasn't even the good kind of arbitrary, where excellent reasons exist for choosing it over all other alternatives, it is just technically not unique. AFAIK, it wasn't even a particularly suitable threshold, and it probably isn't optimal in many cases (for instance, I think it's fair to say that for multiple hypothesis tests, 0.05 is not appropriate). If Fisher ever made some argument why it should be 0.05 and not something else, I'm not aware of it.
But today, we have the benefit of an ocean of knowledge and experience in statistics, as well as having learned a great deal of thinks about how large research communities behave in the long term. For instance, the famous Ioannidis paper, while not concerned with the significance threshold per se, seems like it would have been not wholly irrelevant to Fisher's thinking had he known about it.
Given this, is it possible for us to do better than Fisher? Is there a persuasive argument to be made in favor for adoption of a different threshold? Is there a technique that can be applied to select an appropriate threshold for an experiment that one is planning?