More Principle Component Analysis
In an effort to address the problems encountered in Discriminant Analysis, a different method using Principle Component Analysis was employed. If it is not possible to divide the whole Prairie du Chien into geochemically distinctive subsections, then perhaps it might be more feasible to discover some gradual overall trends throughout the sampling area; for instance, perhaps there might be a trend of a subtle north-to-south increase in one or more elements. If discovered, this might be a useful method for provenance studies.
To test this idea, the Principle Component scores for all of the samples were plotted against the UTM coordinates of each sample location (UTM coordinates are distances in meters north and east from the 1927 North American Datum). The plots of PC2 and PC3 scores vs. northings (Figure 10) do not show any identifiable trends, but there does seem to be a slight trend of increasing PC1 scores from north to south. Similarly, there seems to be a correlation between PC1 and easting distance (Figure 11). There is a gradual increase of PC1 from west to east. As discussed above, the PC1 axis corresponds moderately strongly with lanthanum and samarium (see Table 5), and is positively correlated with all the elements.
The outcrop (and therefore also the sample location) distribution of the Prairie du Chien is strongly controlled by the location of the Mississippi River within the Driftless Area (see Figure 3). Since the river runs from northwest to southeast, the sample locations have a similar distribution. Therefore, in order to explore further the possibility of geographic trends in geochemistry, the PC scores were also plotted vs. the distances in kilometers southeast from an arbitrary point (approximately at Minneapolis). For this analysis, the samples from locations 17 and 18 were excluded, due to their large distance away from the Mississippi River and the southeast-trending spread of sample locations (see Figure 3). When the Principle Component scores were plotted versus their southeast distances, PC2 and PC3 do not show trends, but once again there is a correlation with PC1 (Figure 12).
These correlations of PC scores with compass directions suggest that there is an axis to the geochemical trends, directionally increasing towards the southeast or east-southeast. This information is reinforced by a Canonical Correlation Analysis of the data set. Canonical Correlation Analysis is a method designed to find the mathematical "rule" by which two (or more) dependent variables are correlated. The results of Principle Component Analysis indicate that the geochemical and sample location data are not independent from one another; therefore they make a good candidate for Canonical Correlation Analysis. Such an analysis of the Prairie du Chien data set calculated the axis of maximum geochemical gradient (which provides the optimum correlation to sample location). This gradient axis has an 89.56% correlation with the southeast direction, indicating that the two are virtually identical.
Luedtke (1978) found similar correlations between PC scores and compass directions. Those PC scores appeared to be controlled by the unidirectional increase of just a few elements in particular. In contrast, however, her study found evidence of two distinct perpendicular trends rather than just a single one. It is disappointing that there is not evidence for a similar trend of elements acting in perpendicular directions within the Prairie du Chien. If so, it might be feasible to geochemically pinpoint lithic materials deriving from a particular location, using a "latitude-and-longitude" element scale. As it is, however, it seems that the best that can be achieved is a crude determination of southeasterly distance.
A test of geologic provenance using the PC1 scores was conducted with the INAA data from seven archaeological samples of Prairie du Chien chert from the Vosberg Site near Faribault (see Figure 13). When plotted with the PC1 vs. southeast-distance plot (Figure 14), the mean score for the seven samples appears to place them geographically at the southeast end of the field area. The true southeasting distance of the Vosberg Site is approximately 80 km, however, placing it nearer the northwest end of the field area. The reason for this disagreement is unknown. It is notable that the Vosberg Site is not actually within the outcrop area of the Prairie du Chien. It is possible that the inhabitants of the site brought the lithic materials from somewhere to the southeast, as is suggested by the geochemistry, but there is no independent means to test such a hypothesis. Alternatively, perhaps the raw material was obtained from the stream deposits of a river which had carried the chert cobbles a long distance. Also, the Vosberg Site is a moderately long distance to the southwest from the Driftless Area and the main band of sample locations in this study. Therefore, a third possibility is that the observed trend in PC1 scores might not hold true for chert sources distant from the southeast-trending axis defined in this study, which falls mainly along the Mississippi River.
Figure 13: Location of the Vosberg archaeological site in relation to the sample locations.
Figure 14: Plots of Principle Component Scores versus distance in kilometers southeast from Minneapolis. Vertical bars show the range of values at each sample location, circles with cross bars indicate the sample mean at each location. On the far right is the range of values for archaeological samples from the Vosberg Site. The pair of dashed lines indicate one standard deviation above and below the mean.
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Intro and Background Fieldwork Sample Prep Data Analysis PCA Correspondence Analysis Stepwise DA
Discriminant Analysis More PCA Element Trends Conclusions Bibliography Appendix A: Part 1 Part 2 Part 3 Part 4 Part 5 Appendix B Appendix C