P-value

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is correct. It is the most widely used — and most widely misunderstood — statistic in empirical science. A p-value of 0.05 does not mean that the null hypothesis has a 5% probability of being true. It means that, if the null were true, the observed data (or more extreme data) would occur 5% of the time. The difference is not pedantic. It is catastrophic.

The misinterpretation of p-values as posterior probabilities has produced a literature in which statistically