  Bayes factors are characterized by both the powerful mathematical framework
of Bayesian statistics and the useful interpretation as evidence
quantification. Former requires a parameter distribution that changes by seeing
the data, latter requires two fixed hypotheses w.r.t. which the evidence
quantification refers to. Naturally, these fixed hypotheses must not change by
seeing the data, only their credibility should! Yet, it is exactly such a
change of the hypotheses themselves (not only their credibility) that occurs by
seeing the data, if their content is represented by parameter distributions (a
recent trend in the context of Bayes factors for about one decade), rendering a
correct interpretation of the Bayes factor rather useless. Instead, this paper
argues that the inferential foundation of Bayes factors can only be maintained,
if hypotheses are sets of parameters, not parameter distributions. In addition,
particular attention has been paid to providing an explicit terminology of the
big picture of statistical inference in the context of Bayes factors as well as
to the distinction between knowledge (formalized by the prior distribution and
being allowed to change) and theoretical positions (formalized as hypotheses
and required to stay fixed) of the phenomenon of interest.
