A thoughtful text by William A. Wilson on the replication crisis, including a nice explanation of Bayesian statistics:
Suppose that there are a hundred and one stones in a certain field. One of them has a diamond inside it, and, luckily, you have a diamond-detecting device that advertises 99 percent accuracy. After an hour or so of moving the device around, examining each stone in turn, suddenly alarms flash [...] What is the probability that the stone contains a diamond? [...] if we were to wave the detector over every stone in the field, it would, on average, sound twice—once for the real diamond, and once when a false reading was triggered by a stone. If we know only that the alarm has sounded, these two possibilities are roughly equally probable, giving us an approximately 50 percent chance that the stone really contains a diamond.
once an entire field has been created—with careers, funding, appointments, and prestige all premised upon an experimental result which was utterly false due either to fraud or to plain bad luck—pointing this fact out is not likely to be very popular.
Many defenders of the scientific establishment will admit to this problem, then offer hymns to the self-correcting nature of the scientific method.
The counter attack:
So the dogma goes. But these claims are rarely treated like hypotheses to be tested. Partisans of the new scientism are fond of recounting the “Sokal hoax"—physicist Alan Sokal submitted a paper heavy on jargon but full of false and meaningless statements to the postmodern cultural studies journal Social Text, which accepted and published it without quibble—but are unlikely to mention a similar experiment conducted on reviewers of the prestigious British Medical Journal.
The bottom line:
When cultural trends attempt to render science a sort of religion-less clericalism, scientists are apt to forget that they are made of the same crooked timber as the rest of humanity and will necessarily imperil the work that they do. The greatest friends of the Cult of Science are the worst enemies of science’s actual practice.