In short, p=0.05 means that 5% of no-effect experiments show a false positive.<p>But due to publication bias, negatives are ignored. When there are lots of experiments looking for mostly non-existent effects , the false positives appear ever more commonly than true positives.<p>This is why Bayesians insist on choosing a prior probability. Without it, there is no way to interpret the result of an experiment.<p>The takeaway lesson here, which is horribly underemphasized in school , is that statisitics never answers yes/no questions! Statistics can only give you a <i>function</i> for combining a Prior with an Experiment to obtain a Posterior. Without a Prior (which is subjective; it can never be chosen objectively!), you cannot get a Posterior Probability out of a experiment.