I  just stumbled into a very instructive example which illustrates that p-values should not be misinterpreted as  measures of the probablity with which a research hypothesis is true. In 2011 the OPERA collaboration reported evidence that neutrinos travel faster than light, a finding which violates Einstein’s theory of relativity and if true would have shattered physics as we know it! Their analysis was significant at the 6 sigma level, even more stringent than the accepted but already brutal 5 sigma level of particle discovery (p=3.5 x 10-7). Extraordinary claims require extraordinary evidence ! The results were replicated by the same group, published, and hailed by the world scientific and lay press. A short while later it turned out that the GPS systems were not properly synchronized, and a cable was loose. Neutrinos are back at the speed of light, and we can learn from this that p-values are ignorant of simple systematic errors!