A tutorial on teaching hypothesis testing

How can we teach graduate-level students the principles of hypothesis testing in order to improve their skills inapplication 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 instatistics, 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 moreattractive and accessible to students, a chance game using two dice was used for illustration. We first considered an experimentwith simple hypotheses showing the three inferential principles in an easy way. The experiment was then extended to a morerealistic 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 apprehensionthat current inferential practice is a mixture of different approaches to hypothesis testing