The statistical treatment of correlated bilateral traits in the analysis of cranial material.

At present there is no standardized method to derive frequencies from bilateral non-metric traits. In this paper the commonly used methods are evaluated in light of statistical considerations and degree of sample preservation. In particular, we explore the question of dependence between sides for the bilateral traits. Several workers have tested for bilateral trait correlation in incorrect ways, confusing tests for differences in side frequencies with tests for independence. An easy method to test for independence, using the chi-squared test, is recommended. This test is used on 16 bilateral traits in a large sample of prehistoric carnia from Central California and significant dependence is found for all 16 of these traits. We suggest the traditional method of deriving frequencies be used. Both sides of the cranium should be considered, dividing the number of times the trait occurs by the number of sides available for observation. This method can be used even in poorly preserved samples. Side to side correlation may be compensated for by modifying the constants subtracted in the mean measure of divergence and in the expression for the approximate variance of the mean measure of divergence when the samples are drawn from identical populations.