There is increasing concern that in modern research, false findings may be the majority or even the vast majority of published research claims. However, this should not be surprising. It can be proven that most claimed research findings are false. – John Ioannidis
The argument is from a paper by John Ionnidis, but Alex Tabarrok gives a much easier to read analysis of the fairly simply Bayesian reasoning behind it. Essentially, this is the classic problem of false positives vs. true positives when the condition being tested for is rare in the population (e.g. presence of AIDs in non-high-risk groups, or in this case the truth of a hypothesis).
It might be tempting to argue that the case of a hypothesis under test being true isn’t typically as bad as the general assumptions being made to drive the argument, since the researchers presumably have some thought or intuition that drives them to pick a particular hypothesis to test (they’re not just throwing darts at a board), but consider that works both ways. Despite the common complaint that this or that study is “just another case of science proving what everybody already knows (and so a waste of money)”, I suspect very few researchers deliberately pick hypotheses that are widely believed to be true, particularly if there’s a lot of evidence and research backing up that belief. That’s not, generally speaking, believed to be the way to advance the frontiers of scientific knowledge. But in that case, the sample is biased in the other direction–a random hypothesis to test would include already-known-to-be-true hypotheses in the same proportion that they occur in the population of all hypotheses, so the hypotheses actually attracting attention are less likely to be true than random chance would dictate. Whether the scientist’s intuition towards selecting true hypothesis is a bigger bias than the elimination of all the ones believed to be true is something you can’t really be sure of, so I’d be really cautious about asserting that P(hypothesis is true) must be a lot better than Ionaddis’ calculations allow for.