It always amazes me that *any* scientist uses a p value as large as .05. Let's face it, a 1/20 change of the result being due to chance is way too high for any real confidence in the result.
Instead, what would happen if we started using, say, a maximum p value of .0005?
Now, instead of a 1 in 20 chance of the result being due to chance, we have a 1 in 2000 for it being due to chance. Still, given the thousands of tests being done, there will be some 'false positives' that get through, but many, many fewer than is now the case.
That would greatly increase the overall confidence in our result and, most likely, improve the overall image of the science among the lay public.
The main downside? Some scientists would have to work a lot harder to get publishable results. I bet that would be a good thing.
In particular, way too many results in the medical journals use a p<.05 standard. This, in my mind, is almost criminal. It is also a standard in many psychological journals.