On the application of the averaged correlation matrix in craniometry

The article presents an averaged correlation matrix for 20 craniometric features, calculated for 24 male Eurasian samples. In some cases, correlation matrices calculated for different samples vary significantly; however, the fluctuations in the coefficients are usually random. Most correlation coefficients between craniometric traits have low positive values. The Mantel test, often used to compare matrices, produces incorrect results, since it is insensitive to the relationship between the value of the correlation coefficient and its stability: the lower the value of the correlation coefficient, the higher its random variability. At the same time, averaged correlation matrix based on individual data is similar to the averaged correlation matrices based on worldwide data used by Russian anthropologists at present. The usefullness of averaged correlation matrices for intergroup comparisons has been tested. It was also shown that the use of the averaged matrix for calculating the Mahalanobis distances produces results comparable to the calculations based on individual data. The analyzed samples can represent populations both from the local settlements and territorial communities. That was confirmed by the results of a series of tests for the Eastern European cranial samples, which were not used in the calculation of the averaged matrix. In conclusion some biases in the analysis of correlation coefficients caused by false ideas about their properties are considered.