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

Permutation test for dendrograms and its application to the analysis of mental lexicons