  Given the well-known and fundamental problems with hypothesis testing via
classical (point-form) significance tests, there has been a general move to
alternative approaches, often focused on the Bayesian t-test. We show that the
Bayesian t-test approach does not address the observed problems with classical
significance testing, that Bayesian and classical t-tests are mathematically
equivalent and linearly related in order of magnitude (so that the Bayesian
t-test providing no further information beyond that given by point-form
significance tests), and that Bayesian t-tests are subject to serious risks of
misinterpretation, in some cases more problematic than seen for classical tests
(with, for example, a negative sample mean in an experiment giving strong
Bayesian t-test evidence in favour of a positive population mean). We do not
suggest a return to the classical, point-form significance approach to
hypothesis testing. Instead we argue for an alternative distributional approach
to significance testing, which addresses the observed problems with classical
hypothesis testing and provides a natural link between the Bayesian and
frequentist approaches.
