Alba Regia. Annales Musei Stephani Regis. – Alba Regia. Az István Király Múzeum Évkönyve. 20. 1980 – Szent István Király Múzeum közleményei: C sorozat (1983)
Tanulmányok – Abhandlungen - Bartosiewicz László – Choyke, A. M.: Numerical classification of cattle astragali from pit 55 at Lovasberény-Mihályvár. p. 37–42.
Material and method Astragalus (talus, knucklebone) is a short bone from the tarsal region of the hind leg. As other bones of this joint it ossifies rather late (SCHMID 1972). According to hypothesis 2 however, it should much rather display changes in proportions than in absolute size during ontogeny. On the other hand, the proportions most probably reflect the stature of the animal, and obviously are not heavily influenced by the sometimes oscillating live weight of the individual. In order to detect the patterns of variability within the sample 13 measurements were taken on each bone, 3 of which were later exluded from the calculations as inaccurate. The 10 variables (Fig. 1) were subjected to three kinds of multivariate analyses which and used in the following hierarchy: 1. Factor analysis 2. Cluster analysis of cases 3. Stepwise discriminant analysis The computation was carried out using the Biomedical Programs (BMDP P series, Health Sciences Computing Facility — UCLA). Further technical details of such calculations are widely discussed in the literature (DORAN — HODSON 1975; WILLIAMS 1979; EVERITT 1980 for example.) Marks of butchering and heat treatment characteristic for this bone sample have already been analysed using two-way frequency tables (DARLINGTON 1974) and published in a separate paper (Choyke —Bartosiewicz 1980/81). Results The factor analysis was applied first, in order to understand the possible structure of variables. The univariate statistics and coefficients of correlation of this calculation are shown in Tables 2—3. The almost uniformly high coefficients of correlation between the measurements on these short bones indicate that there was no possibility for separating independent factors for groups of variables: The measurements taken change more-or-less harmonically with each other. In order to explore the pattern emerging from the previous calculation the data were subjected to a cluster analysis which indeed outlined three independent groups under the critical standard value of 2 in addition to a few "miscellaneous" bone specimens. Although the dendrogram in Fig, 2 shows that the clusters were not separated on the basis of size only but also reflect differences in proportions, the previous factor analysis showed that there is a good reason to label these clusters (drawn with continuous lines) as "small", "medium", and "large" individuals. The majority of results obtained favor hypothesis 2. However, before rejecting hypothesis 1 (H 0 ) a stepwise discriminant analysis was carried out to verify the differentiation outlined by the two former computations. The three groups to be distinguished were formed using the evidence of the dendrogram. Aside from the three clearly Fig. 1: Astragalus measurements ranked on the basis of factor loadings of the single factor obtained ("size")'. 1 greatest lateral length; 2 chord of the lateral trochlea; 3 chord of the medial trochlea; 4 distal width; 5 lateral depth; 6 proximal width; 7 smallest length; 8 width of the plantar articular surface; 9 medial depth; 10 greatest medial length. V = norma ventralis (plantaris); D m norma dorsalis; L = norma lateralis; M = norma medialis separable clusters, all the remaining bones were included in one or the other of the groups. At the beginning of this calculation an F-test was computed to select the variable with the most distinctive value: greatest lateral length. In the following steps further variables were included until the differentiation was completed. Parameters of this computation were as follows: Variable: greatest lateral length, F value: 55.3614, U statistic: 0.2702, Degrees of freedom: 2, 41 The first thing of note is that in accordance with the results of the factor analysis measurements directly reflecting size have the most discriminating value. As far as the three groups shown in Table 4 are concerned the classification matrix in Table 5 shows that the results largely correspond to those obtained during the previous analyses. Aside from 2 incorrect classifications the presence of groups may be rather clearly seen. Fig 3 shows the canonical variables represented by the codes of clusters and the group of measurements respectively plotted against each other. The distribution of data points provides a final evidence of the subdivision of the sample. 38
