  A key goal of empirical research in software engineering is to assess
practical significance, which answers whether the observed effects of some
compared treatments show a relevant difference in practice in realistic
scenarios. Even though plenty of standard techniques exist to assess
statistical significance, connecting it to practical significance is not
straightforward or routinely done; indeed, only a few empirical studies in
software engineering assess practical significance in a principled and
systematic way.
  In this paper, we argue that Bayesian data analysis provides suitable tools
to assess practical significance rigorously. We demonstrate our claims in a
case study comparing different test techniques. The case study's data was
previously analyzed (Afzal et al., 2015) using standard techniques focusing on
statistical significance. Here, we build a multilevel model of the same data,
which we fit and validate using Bayesian techniques. Our method is to apply
cumulative prospect theory on top of the statistical model to quantitatively
connect our statistical analysis output to a practically meaningful context.
This is then the basis both for assessing and arguing for practical
significance.
  Our study demonstrates that Bayesian analysis provides a technically rigorous
yet practical framework for empirical software engineering. A substantial side
effect is that any uncertainty in the underlying data will be propagated
through the statistical model, and its effects on practical significance are
made clear.
  Thus, in combination with cumulative prospect theory, Bayesian analysis
supports seamlessly assessing practical significance in an empirical software
engineering context, thus potentially clarifying and extending the relevance of
research for practitioners.
