It is conventionally thought that a small p-value confers high credibility on the observed alternative hypothesis, and that a repetition of the same experiment will have a high probability of resulting again in statistical significance. It is shown that if the observed difference is the true one, the probability of repeating a statistically significant result, the 'replication probability', is ...

It is noteworthy how many people will respond, when conversation turns to mathematics or statistics, that they personally have no aptitude and struggled with the subject since school. Such a reacti...