  A novel type of permutation tests for dendrogram data is studied with respect
to two types of metrics for measuring the difference between dendrograms.
First, the Frobenius norm is used, and we prove the consistency and efficiency
of the permutation tests. Next, the geodesic distance on a dendrogram space is
used. The uniqueness of the geodesics on every dendrogram space is proved and
some existing algorithms for computing geodesics are applied. Mental lexicons
of English words are analyzed as an application example of the proposed
permutation tests. The difference of mental lexicons between native and
non-native English speakers is examined by analyzing sorting task data that
used English words taken from various word classes.
