There are many approaches to hypothesis testing. The well-known approach of p-values has been drawn into question and even controversy in more recent years, even though criticisms reportedly date back at least as far as 1954 (Dowe, 2008a, sec. 1, pp549-550).
Discussion of how to do this using the Bayesian information-theoretic minimum message length (MML) approach (Wallace and Boulton, 1968; Wallace and Dowe, 1999a; Wallace, 2005) are given in Dowe (2008a, section 0.2.5, page 539, and section 0.2.2, page 528), and Dowe (2011, pages 919 and 964).