Comparing groups

One common task in statistical analysis is to compare groups; for example, we may be interested in how well a patient responds to some drug, the reduction of car accidents by the introduction of a new traffic regulation, or students' test responses under different teaching approaches, and so on. Sometimes this type of question is framed under the hypothesis-testing scenario, with the goal of declaring a result statistically significant. Relying only on statistical significance can be problematic for many reasons: on one hand, statistical significance is not necessarily practical significance; on the other, a really small effect can be declared significant just by collecting enough data. Also, the idea of statistical significance is connected to computing p-values. There is a long record of studies and essays showing that, more often than not, p-values are used and interpreted the wrong way, even for scientists who use statistics on a daily basis. Under the Bayesian framework...