Application of the Multivariate Runs Test to Compositional Data

Autor: W. E. Sharp
Rok vydání: 2006
Předmět:
Zdroj: Mathematical Geology. 38:1017-1025
ISSN: 1573-8868
0882-8121
DOI: 10.1007/s11004-006-9059-3
Popis: The graph median has recently been proposed (Sharp, 2006) as an alternative measure of central tendency in those instances when the arithmetic average is not a part of the data set. This property was illustrated with ternary diagrams by using a series of five three-component compositional data sets all of which had the same mean, but greatly differing patterns in their compositions. For these sets, a comparison of their means and, except for the case in which all compositions (hongite2) fell on the same line, a comparison of their variance would be of no value. Contemplation of this fact, suggested the need for a simple method that determines the extent to which two data sets with several components are coincident. Suppose one visualizes each component of a composition as being plotted along a separate coordinate axis, then an individual compositon can be represented as a point in a space of three or higher dimension and the data set as a whole when plotted would form a cloud of points. If the two data sets are statistically the same, the two clouds of points should be of similar size, shape and internal point distribution. A test for this can be conceived as follows. Merge the two clouds of points into one and then connect each pair of points in the combined cloud with the one set of lines such that the total length of the lines is a minimum. In graph theory, the points are termed nodes, the lines as edges, the set of connected lines as a tree and the set of lines having a minimum total length as a minimum spanning tree (e.g. Reingold, Nievergelt, and Deo, 1977, chap. 8). If the two data
Databáze: OpenAIRE
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