Model Assisted Statistics and Applications 7 (2012) 143–157 143 DOI 10.3233/MAS-2011-0222 IOS Press Teaching Statistics A tutorial on teaching hypothesis testing W.J. Post ∗ , M.A.J. van Duijn and A. Boomsma Faculty of Behavioural and Social Sciences, University of Groningen, Groningen, The Netherlands Abstract. 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. Keywords: Fisher, Neyman-Pearson, Bayesian inference, hypothesis tests, p-values, likelihood ratio 1. Introduction As statisticians in a faculty of behavioural and social sciences, we work with colleagues and students whose first interest is not statistics but rather psychology, education or sociology. For them, statistical analysis is primarily about how to get substantive results and conclusions. Hypothesis testing procedures are performed rather routinely and results of those tests are summarized simply by interpreting non-significant findings as support for the null hypothesis, which implies that the presumed theory is false. Significant results, on the other hand, are interpreted bluntly as proof of the validity of the theory, or of the existence of ‘an effect’ of whatever size; see Snijders [28], who discussed several interpretative problems in hypothesis testing. Most of our students do not acknowledge that their significant or non-significant findings may be due to chance, i.e., there are errors of the first and second kind, although they may mention lack of power when hypothesized effects are not found. We would like to contribute to a more thoughtful application and interpretation of hypothesis testing procedures. In line with the bachelor education endpoints in the social sciences, teaching statistics largely amounts to instructing students how to compute descriptive statistics, and to explain the basic principles of estimation and hypothesis testing. We strongly believe, however, that master students should be trained to critically assess the statistical design and analysis. A critical attitude is even more important for research master students who may pursue a Ph.D. education and become academic researchers. In our faculty, this is a selective group of high-achieving and motivated students. They are heterogeneous, however, with respect to discipline, country of origin (typically about half of them are foreign students), and most importantly, statistical training. ∗ Correspondence author: Grote Kruisstraat 2/1, 9712 TS Groningen, The Netherlands. Tel.: +31 503 636 588, Fax: +31 503 636 521, E-mail: w.j.post@rug.nl. ISSN 1574-1699/12/$27.50  2012 – IOS Press and the authors. All rights reserved