A tutorial on teaching hypothesis testing

How can we teach graduate-level students the principles of hypothesis testing in order to improve their skills in application and interpreting hypothesis test results? This was one of the main challenges in our course Applied Statistics. Although most students, all potentially future researchers in social and behavioural sciences, were not specifically interested in statistics, it seemed a good idea to teach them the essentials of three approaches to statistical inference introduced by Fisher, Neyman and Pearson, and Bayesian statisticians. To make the rather subtle differences between the inferential approaches and associated difficult statistical concepts more attractive and accessible to students, a chance game using two dice was used for illustration. We first considered an experiment with simple hypotheses showing the three inferential principles in an easy way. The experiment was then extended to a more realistic setting requiring more complicated calculations (with R-scripts), to satisfy the more advanced students. We think that our lectures have enabled a deeper understanding of the role of statistics in hypothesis testing, and the apprehension that current inferential practice is a mixture of different approaches to hypothesis testing.