Crossing the Borders: New Methods and Techniques in the Study of Archaeological Materials from the Caribbean

60 / Knippenberg and Zijlstra
Analysis is considered most suitable (Craddock et al. 1983; De Bruin et al. 1983;
Glascock et al. 1998; Luedtke 1979; Sieveking et al. 1972). Klecka (1980:7) defines
Discriminant Analysis as “a statistical technique, which allows the researcher to
study the differences between two or more groups of objects, with respect to several
variables simultaneously.” In relation to this study, the sources of chert material
are the groups, and the different trace element concentration values represent
the variables. This technique can be applied in two different ways: (1) Descriptive
Discriminant Analysis that is used in interpreting group differences; and (2) Predictive
Discriminant Analysis that is used for classification (assignment 2 ) of cases
to groups. The latter application has been widely used in provenance studies for
stone materials.
In short, Discriminant Analysis (DA) determines which factors contribute most
to group separation. It identifies functions, called canonical discriminant functions,
that are linear combinations of the original variables. These functions maximally
enhance group separation. The classification technique of DA calculates a
centroid for each group, which is the mean value in multidimensional space based
on values obtained from the canonical discriminant functions. It then compares
the distance of the canonical value of an unknown case (an artifact for which one
wants to identify the source) to the centroids of the different groups. This distance
(D) is called the Mahalanobis distance. The artifact will be assigned to the group
for which D 2 is smallest.
In this study, 12 trace elements were used for the discrimination of sources and
for assigning artifacts to sources, as their concentrations appeared to be above the
detection limit in most cases, and as their measurement provided relatively precise
results. The elements are: Lithium (Li), Sodium (Na), Potassium (K), Magnesium
(Mg), Calcium (Ca), Barium (Ba), Titanium (Ti), Vanadium (V), Chromium (Cr),
Manganese (Mn), Iron (Fe), and Aluminum (Al).
In order to evaluate how well sources in this study are discriminated, only the
source samples were entered in first instance, and tests were performed on the classification
results, using the leave- one- out, or jack- knife method (Glascock et al.
1998). It appears that the success of individual assignment to the sources is moderately
well. Using cross- validation classification in the SPSS statistical program
produced a correct assignment rate of just above 73 percent. Different researchers
working on northwestern European flints found similar or lower success rates
(Craddock et al. 1983; De Bruin et al. 1983). This relatively low assignment rate as
compared to, for example, obsidian studies (see Glascock et al. 1998) can be attributed
to relatively large intrasource and relatively low intersource variation, as is in
general the case for chert and flints. 3
Considering this moderate correct assignment rate on a source specific level,
the next step is to see how well the sources from the three islands can be discriminated.
It appears that approaching this problem using two steps produces the best
results. By first discriminating Puerto Rico from the two Lesser Antillean islands,
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