Worked Example - Japanese Pottery
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Demonstration data set: Jomon Hall.csv.
Reference: Hall, M. E., 2001. Pottery styles during the early Jomon period: geochemical perspectives on the Moroiso and Ukishima pottery styles. Archaeometry 43, 59-75.
This example is based on the study by Hall (2001) of pottery shards from the early Jomon period (c. 5000±2500 BC). Energy-dispersive X-ray fluorescence was used to determine the concentration of 15 minor and trace elements in 92 pottery sherds. The sherds came from four sites in the Kanto region and belong to either the Moroiso or Ukishima style of pottery.
The author reasoned that if the pottery were locally produced, we should expect to find statistically significant differences in the chemical composition between potsherds from different sites. If there are no differences between sites, then we can assume that the Jomon potters utilized raw materials that were geochemically similar, or that the pottery was part of a trade/exchange/redistribution network between settlements. For each sherd the elemental composition of barium (Ba), copper (Cu), gallium (Ga), iron (Fe), lead (Pb), manganese (Mn), nickel (Ni), niobium (Nb), rubidium (Rb), strontium (Sr), thorium (Th), titanium (Ti), yttrium (Y), zinc (Zn) and zirconium (Zr) were measured.
Preliminary data examination and transformation
The concentration of the elements present varied greatly from about 105 ppm for iron (Fe) to around 10 ppm for yttrium (Y). The author therefore undertook a log 10 transformation on the data to reduce the dominance of Fe and Ti in the analysis. Given the 5 orders of magnitude difference in concentrations and the fact that the data set holds no zeros, a log transformation is a good choice. Niobium was removed from the data set prior to analysis as it was generally below the detectable limit.
The use of the correlation matrix
PCA was done on the correlation matrix of the log-transformed data. By using the correlation matrix the author was giving all the elements the same influence on the final ordination. This is the correct choice if it is believed that all elements can potentially equally contribute to the identification of similarities between sherds, irrespective of concentration. In fact for these data the author would have reached substantially similar conclusions if the variance-covariance matrix of log-transformed data had been used instead.
As shown in the table below, the first 3 axes explained about 57.89 % of the total variability in the data set. The sum of all the eigenvalues, which is a measure of the total variability, is 14, which is simply the sum of the number of variables used in the analysis. This summation is always true when a correlation matrix is used. Therefore the percentage variability explained by the largest eigenvalue is 4.713/14 x 100 = 33.66%.
These results suggest that much of the variability in elemental composition can be expressed in 3 dimensions. The first 4 dimensions are probably meaningful (eigenvalues > 1).
An examination of the 3 2D plots possible for the 3 largest components showed that the position of the sherds in the 2 dimensional space defined by the 1st and 3rd principal components separated the sherds into the 4 localities (Fig 1). Four sample outliers in the PCA were a:mb:002, k:uk2:008, n:uk:137 and s:mb:007. For example, the sherd s:mb:007 is represented by the grey square on the far right of the plot. By repeating the analysis with the outliers removed (Fig 3) we can see more clearly the grouping of the shards between the 4 sites. In the figure, each of the sites is coded as a different colour. You will see for example that the blue squares, representing the Narita 60 site are clustered in a single discrete area.
Figure 1: PCA ordination of Jomon potsherds. Red – Aryoshi-kita, Yellow – Kamikaizuka, Blue - Narita 60 and Grey - Shouninzuka.
Figure 2: A plot of the eigenvectors for the 14 elements used for the PCA.
The plot of the eigenvectors in Fig 2 shows that Principal axis 1 is a measure of the concentration of the elements Zn, Ba, Mn, Zr, Ga, Cu, Ni, Fe, Y and Ti present, with sherds to the left (negative direction) of the axis having the largest concentrations. Axis 3 is a measure of Sr, Rb, Th and Pb concentration with the greatest concentrations at the top (positive direction) of the axis.
The samples were also classified by pottery style – Red is Moroiso A, Yellow Moroiso B and Blue Ukishima. By comparing the plot showing the sites and the styles it is apparent that the Ukishima pottery is found at all the sites. Note that there is some difference in the elemental composition in the pottery styles, with Moroiso sherds having generally higher concentrations of all the elements measured.
Figure 3: PCA ordination of Jomon potsherds using the Variance-covariance matrix. Red – Aryoshi-kita, Yellow – Kamikaizuka, Blue - Narita 60 and Grey - Shouninzuka.
Hall (2001) concluded that Principal Component Analysis indicates that there are four major groups in the data set, which correspond to site location. This indicates the majority of Early Jomon pottery found at four sites in Chiba Prefecture was made from locally available raw materials. While the Kamikaizuka and Shouninzuka groups overlap, both sites are less than 10 km apart and their potters could have shared the same raw material sources.
For sites having both Moroiso and Ukishima pottery, both styles of pottery were made from the same or geochemically similar raw materials. This suggests that both styles were probably made at the same site, and indicates that if the different pottery styles are reflecting ethnic identity, then intermarriage between ethnic groups is occurring. Alternatively, the pottery styles could be reflecting some sort of social interaction between groups.