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4.7 Multivariate Statistical Analysis of Fine Fraction Results 



Multivariate statistics were used to evaluate whether there were statistically 

 significant differences between the three layers (CDM, UDM, and AMB) classified from 

 the postcap cores. As described in Section 3.10, several statistical methods were used, 

 with the primary difference dependent on how the data were prepared. For clustering and 

 MDS results (Section 4.7.1), the samples were analyzed prior to the layer classifications. 

 Two statistical tests were conducted on the sample groups using the classifications derived 

 after visual and microfossil results were compiled: an analysis of similarities test (Section 

 4.7.2), and an evaluation of discriminant statistics (Section 4.7.3). The analysis of 

 similarities tested the null hypothesis that there was no difference between the UDM and 

 CDM layers from the postcap cores. The discriminant statistics were then utilized to 

 visually show the strength of the layer differences using both microfossil and mineralogical 

 results. 



4.7.1 Clustering and Multi-Dimensional Scaling Results 



The fine fraction mineralogy and microfossil results were analyzed to determine the 

 statistical similarity (cluster) and dissimilarity (MDS ordination) between samples, and to 

 quantitatively evaluate the strength of any resultant clustering among the samples. More 

 detailed information on the statistical methods is available in Section 3.10. The results are 

 provided in a variety of graphical formats in the figures below. In order to better interpret 

 the information, we first briefly describe the statistical output, and how it is presented. 



The first analysis that we conducted, using the PRIMER clustering program (Bray- 

 Curtis similarity index), independently determined the similarities between sample data 

 points based on multiple variables, and then grouped them accordingly to generate a 

 similarity matrix. The matrix of samples was created with the similarities linked, with the 

 links shown in a hierarchy and displayed on a dendrogram. The dendrograms provided 

 below display the agglomerate clustering based on similarity. The higher the level of 

 groupings on the dendrogram, the more similar those groups of samples were, relative to 

 the mineralogy composition or the microfossil community structure. 



The second test, a non-metric multi-dimensional scaling (MDS), provided an 

 ordination, or map, of samples showing the inter-relationships between samples on a 

 continuous scale. The ordination plots shown in the results below were constructed by an 

 iterative procedure, which successively refined the positions of the samples to reflect the 

 similarity relations between individual samples. The MDS method was used to produce a 

 two-dimensional representation of the data from a three-dimensional dataset as shown in 

 the ordination plot, and calculated a value called "stress" which provided an indication of 

 the fit of the data in two-dimensional (2D) space. Stress values of up to 0. 1 correspond to 

 good to excellent 2D representation, values of up to 0.2 indicate the results are useful but 



The Portland Disposal Site Capping Demonstration Project, 1995-1997 



