It's not science that is the problem. It's that biology considers a 95% confidence sufficient. Considering how many studies are done each year, this virtually guarantees incorrect results.
The reason they do that is that it's impossible to get better results, they just can not do enough trials. So they are stuck.
a) all data, everywhere in the world, including negative results, was published regardless of funding/publication.
b) someone actually looked at that data, normalized it, and used it to assess the real significance of every result, in a sane manner (e.g. by using a bayesian inference with some reasonably behaving universal prior).
Neither a, b will ever happen, and both are essential.
(note: publication of all data is not a sufficient requirement: if 20 independent labs each do the same random experiment, one of them is expected to have a 95% confidence, and when they publish all their data, it consists of that one experiment that seems legit. This _will_ and _already does_ happen by chance)