Natalia N. Goncharova

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 intergroup 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. © 2023. This work is licensed under a CC BY 4.0 license.

Introduction. The article analyzes materials dated to the 16^th–17^th centuries came from Smolensk. This period turned out to be one of the most complex and eventful in the history of the region, that's why every new detail is significant for the study. For a long time, Smolensk functioned as a boundary city and also as an important trade hub between the Muscovite Tsardom and the Polish-Lithuanian Commonwealth; so, the composition of its population may reflect the influence of the western neighbors.

Materials and methods. There were examined the craniological materials discovered during the excavations at the Pyatnitsky district of the city in 2012. The necropolis dates back to the turn of the 16^th–17^th centuries, it is located on the high bank of the Dnieper near the fortress wall of the Smolensk Kremlin. The materials include 17 male and 19 female skulls. Classical and multidimensional biometric methods were used as statistical approaches.

Results. The comparison beetween the studied sample and the other sample of the 12^th century city population known from the literature has showed their high similarity, although the later sample tends to be slenderer. Statistically significant differences were recorded only for certain parameters of the skull.

The comparison with the aggregated sample of the rural Smolensk region population dated to the 18^th–19^th centuries also revealed a significant difference for the cranial length and height and some parameters of the facial skeleton. Discriminant analysis showed a quite unique status of the studied sample, which differs from both synchronous urban groups and later samples of the rural population of the central region. There are also no processes of macrosomization observed for it.

Conclusion. The absence of significant differences for most characteristics between the studied sample and the urban population of the 12th century can indicate the continuity of the morphological type of the Smolensk urban population. On the other hand, the intermediate position of the studied sample in relation to early and late comparative materials can indicate that the studied sample represents recent settlers from the rural area.

© 2024. This work is licensed under a CC BY 4.0 license

Introduction. The task of differentiating groups using various statistical methods remains relevant due to the limitations often encountered with standard algorithms. Some of these limitations, such as the assumption of normal distribution of traits and the absence of high correlations between them, can be circumvented by the method based on step-wise partitioning – decision trees.

Materials and methods. In this study, this method was tested on 15 linear dimensions of the skull and 16 indices calculated based on them. The entropy index was chosen as the criterion of heterogeneity. The craniometric features used correspond to the standard methodology adopted in Russian anthropology. The data consisted of average values of craniometric dimensions from 39 ethno-territorial groups from 13 macro-regions of the Old World.

Results and discussion. The results of the differentiation show that indices have a greater weight than linear features. Five linear dimensions and seven indices participated in the differentiation. Three indices were based on the overall dimensions of the braincase (M.1, M.8, M.17), and four indices included the bizygomatic width (M.45). The first split occurs based on the transverse facial index (46:45), separating the groups of Northern, Middle, Central Asia, and Europe from the groups of Africa, Eastern, Southeast, and Southern Asia.

Conclusion. The study demonstrates the high differentiating ability of indices, particularly the transverse facial index, fronto-zygomatic index, and height-length index. The iterative differentiation system allows for a more informative separation of groups, as different combinations of features demonstrate effectiveness at different hierarchical levels of taxonomy. © 2025. This work is licensed under a CC BY 4.0 license