Comparability of results from canonical discriminant analysis based on different input data

Abstract

Introduction. Canonical discriminant analysis, based on the mean values of the traits, is widely used by anthropologists. These analyses use standard deviation means, as well as standard correlation coefficients. The question of the comparability of the results of such analysis with the results based on individual values remains open. Moreover, the existing inter-group variability in correlation coefficients can lead to altered analysis results when applying the correlation matrix calculated for the specific under analysis groups. This study compares the results of three variants of the canonical discriminant analysis: based on individual data, based on average values and a generalized (species-specific) correlation matrix, and based on average values and a regional (calculated for a certain region) correlation matrix. Materials and methods. Data from 48 ethno-territorial groups from the Old World were used. The series are dated close to modern times, from the 16th to the 20th century. Twenty-five craniometric linear features have been measured. For canonical analysis on individual data we used the R language package, and for average data analysis the MultiCan software was used. Results. The results of the two analyses performed on individual data and on average data turned out to be quite similar. A comparison of the results of a series of discriminant analyses carried out on samples of the three major races using different correlation matrices reveals some small differences in the mutual arrangement of groups. In general, the distribution of samples in the scatter plots, as well as the standardized coefficients of discriminant functions coincide, regardless of the type of initial data. Conclusion. In general, it may be concluded that the use of both individual values and sample averages in most cases leads to the same results. When individual values are used, the results may be distorted as a result of a strong reduction in the number of samples. Also, sample differentiation in this case is strongly influenced by a higher real intra-group variability.