This is a somewhat poorly formed question but the problem it
represents has troubled me several times in my career. Essentially
many theories may state that a particular phenomenon exists either as
a dimension or as a set of discrete categories. For example Reversal
Theory in psychology states (amongst other things) that a person is
either in a telic (purpose driven, arousal avoiding, future oriented)
mode or in a paratelic (activity driven, arousal seeking, present
oriented) mode and that people can't be somewhere "inbetween" the two
modes. So Reversal theory is positing a set of two discrete categories
and strongly claims that all people are in one or other of the two
states and that there is no continuum between them. Similarly Fulda
developed a mathematical model of the pull of temptation and asserts
that the model works on discrete moments of thought (in other words
the probabilities of temptation that are being modelled are discrete
and not continuous). In my experience it is really hard to devise
tests for claims of this kind. I wondered whther there are any
existing statistical tests designed to to test hypotheses of this
kind, or whether there are procedures and designs suitable for testing
such claims?

Lance