  The deviation test belong to core tools in point process statistics, where
hypotheses are typically tested considering differences between an empirical
summary function and its expectation under the null hypothesis, which depend on
a distance variable r. This test is a classical device to overcome the multiple
comparison problem which appears since the functional differences have to be
considered for a range of distances r simultaneously. The test has three basic
ingredients: (i) choice of a suitable summary function, (ii) transformation of
the summary function or scaling of the differences, and (iii) calculation of a
global deviation measure. We consider in detail the construction of such tests
both for stationary and finite point processes and show by two toy examples and
a simulation study for the case of the random labelling hypothesis that the
points (i) and (ii) have great influence on the power of the tests.
