  Given two relations containing multiple measurements - possibly with
uncertainties - our objective is to find which sets of attributes from the
first have a corresponding set on the second, using exclusively a sample of the
data. This approach could be used even when the associated metadata is damaged,
missing or incomplete, or when the volume is too big for exact methods. This
problem is similar to the search of Inclusion Dependencies (IND), a type of
rule over two relations asserting that for a set of attributes X from the
first, every combination of values appears on a set Y from the second. Existing
IND can be found exploiting the existence of a partial order relation called
specialization. However, this relation is based on set theory, requiring the
values to be directly comparable. Statistical tests are an intuitive possible
replacement, but it has not been studied how would they affect the underlying
assumptions. In this paper we formally review the effect that a statistical
approach has over the inference rules applied to IND discovery. Our results
confirm the intuitive thought that statistical tests can be used, but not in a
directly equivalent manner. We provide a workable alternative based on a
"hierarchy of null hypotheses", allowing for the automatic discovery of
multi-dimensional equally distributed sets of attributes.
