ABSTRACT
The likelihood ratio is a ratio of probabilities but should not be confused with the odds, another ratio of probabilities. The odds that something will happen is equal to the probability that it will happen divided by the probability that it will not happen. While the posterior odds is more informative than the likelihood ratio, a likelihood ratio is more informative than a p value. That is because the likelihood ratio can be multiplied by a prior odds to give the posterior odds, but there is no general formula for adjusting the p value according to the prior probabilities. However, treating p values as data leads to useful estimates of posterior probabilities. In general, a method of estimating all prior probability distributions on the basis of data is called an empirical Bayes method.
