  Lexical resemblances among a group of languages indicate that the languages
could be genetically related, i.e., they could have descended from a common
ancestral language. However, such resemblances can arise by chance and, hence,
need not always imply an underlying genetic relationship. Many tests of
significance based on permutation of wordlists and word similarity measures
appeared in the past to determine the statistical significance of such
relationships. We demonstrate that although existing tests may work well for
bilateral comparisons, i.e., on pairs of languages, they are either infeasible
by design or are prone to yield false positives when applied to groups of
languages or language families. To this end, inspired by molecular
phylogenetics, we propose a likelihood ratio test to determine if given
languages are related based on the proportion of invariant character sites in
the aligned wordlists applied during tree inference. Further, we evaluate some
language families and show that the proposed test solves the problem of false
positives. Finally, we demonstrate that the test supports the existence of
macro language families such as Nostratic and Macro-Mayan.
