  In many domains, data measurements can naturally be associated with the
leaves of a tree, expressing the relationships among these measurements. For
example, companies belong to industries, which in turn belong to ever coarser
divisions such as sectors; microbes are commonly arranged in a taxonomic
hierarchy from species to kingdoms; street blocks belong to neighborhoods,
which in turn belong to larger-scale regions. The problem of tree-based
aggregation that we consider in this paper asks which of these tree-defined
subgroups of leaves should really be treated as a single entity and which of
these entities should be distinguished from each other.
  We introduce the "false split rate", an error measure that describes the
degree to which subgroups have been split when they should not have been. We
then propose a multiple hypothesis testing algorithm for tree-based
aggregation, which we prove controls this error measure. We focus on two main
examples of tree-based aggregation, one which involves aggregating means and
the other which involves aggregating regression coefficients. We apply this
methodology to aggregate stocks based on their volatility and to aggregate
neighborhoods of New York City based on taxi fares.
