An International Journal of Epidemiology has a policy of publishing papers about drug trial results only if the conclusion about the drug’s effectiveness (or lack thereof) holds at the 95% confidence level. The editors and reviewers carefully check that any trial whose results they publish was properly performed and accurately reported. They are also careful to check that trials whose results they publish have been conducted independently of each other.
The editors of the Journal reason that under this policy, their readership can be confident that at most 5% of the published studies will be mistaken. Later, the editors are embarrassed —and astonished —to learn that every one of the 20 drug trial results they published during the year was wrong. The editors thought that because the trials were conducted independently, the probability of publishing 20 wrong results was negligible, namely, (1/20)20 < 10-25.
Write a brief explanation to these befuddled editors explaining what’s wrong with their reasoning and how it could be that all 20 published studies were wrong.