  We discuss the conditions under which Scan Statistics can be fruitfully
implemented to signal a departure from the underlying probability model that
describes the experimental data. It is shown that local perturbations
(``bumps'' or ``excesses'' of events) are better dealt within this framework
and, in general, tests based on these statistics provide a powerful and
unbiased alternative to the traditional techniques related with the chi2 and
Kolmogorov distributions. Approximate formulas for the computation of Scan
Statistics in the range of interest for high energy and nuclear physics
applications are also presented.
