Dr. T. Tóth szerk.: Studia historico-anthropologica (Anthropologia Hungarica 21. Budapest, 1990)

MATERIAL AND METHODS Comparative analyses were carried out on the material of ten series excavated in the Central Danubian Basin (Fig. 1). The first eight series belong to the Avar period, the last two are Arpadians. The same cluster analyses were executed with three different data sets. The series were characterized by male mean values. The first series of examinations was based on 9 skull measurements (MARTIN 1, 5, 8, 9, 17, 45, 48, 52, 54). Craniological mean values were taken from the original publications (Table 1). The next sequence of examinations was based on 6 long bone measurements (MARTIN Humerus 1, 7, Femur 1, 8, Tibia 1, 10b). Postcranial mean values of the Avar samples were taken by FÓTHI while those of the Arpadian Age series were also utilized from the original publications (Table 2). In general examinations were based on the data of right-hand side long bones. At the end postcranial indices were applied for the same purpose (robusticity indices of humerus, femur and tibia). Stature and body weight were calculated according to the formula of DEBETS & DURNOVO (1971). Finally, the so-called Livi index was also calculated. (Table 3). The ever present problem of historical anthropology emerged: the application possibilities of multivariate statistical methods for relatively small samples. As cranial and body constitution can be described only with a large number of measurements, we had to adhere to the use of a large number of variables. Hierarchic cluster analysis was applied for classifying the series. The essence of our method of analysis is to execute a great number of different nature hierarchic cluster analyses that can check up and complement each other. We did not apply the usual statistic methods for establishing joining links among population groups - because of the small number of samples and the great number of variables. We accepted only those results which kept on occurring in the various cluster analysis dendograms as a tendency. The dendograms were analyzed with special attention to the nature of the methods applied. Four different types of distance were utilized: Euclidean, Minkowski, Chebisev (or Maximum) and Mahalanobis (DURAN & ODELL 1974). Cluster distances were also established in four different ways: nearest neighbour, furthest neighbour, group average and centroid methods (JAMBU & LEBEAUX 1983). The data were either transformed in the 0-1 interval or standardized (expectable value 0, spread 1). Approximately two hundred cluster analyses were performed. We introduce some of them in brief. RESULTS Distribution of the series analyzed is shown in Figure 1. We wanted to get answers for two questions: 1. Are there any regional differences among the samples? 2. How do the results of the analysis of postcranial absolute measurements and indices coincidence with those of cranial analysis? The first series of examinations was based on 10 skull measurements. When applying 0,1 data transformation, nearest neighbour method and Euclidean distance we obtained two groups (Fig. 2a). The same dendrogram occurred with Minkowski distance and the same again with the Maximum distance (Fig. 2b) which is completely different from the previous ones. The next series of clustering was based on the same data but was produced by an absolutely different strategy, ft was the furthest neighbour method with Euclidean (Fig. 2c), Minkowski and Maximum methods (Fig. 2d). These dendrograms presented a surprising coincidence of results. Dendograms made by group average and centroid methods produced no new results when compared to the previous ones. All of them concurred with some of the figures already presented. When transforming data by standardization we arrived at the same results again. Based on them we may say that Homokmégy, Üllő I and II formed a closed homogeneous group. Series 1 (Alattyán) was loosely connected to them. Fészerlak, Környe, Szabolcs, Toponár and Tiszalök made up another coherent, though looser cluster. Tiszavasvári was markedly different from the others.