Exploratory Graphical Techniques for Ranked Data,
SOUTHERN METHODIST UNIV DALLAS TX
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Graphical methods are critically needed to display frequency distributions for fully ranked data. Fully ranked data occur, for example, when judges are asked to rank n items, possibly with pseudoranks, in order of preference. Each observation is a permutation of the n distinct pseudoranks, and the resulting set of frequencies is a function on Sn, the symmetric group of n elements. Because Sn does not have a natural linear ordering, graphical methods such as histograms and bar graphs cannot be used to display frequency distributions for ranked data. Other existing graphical methods for rankings include multidimensional scaling, minimal spanning trees, and nearest neighbor graphs as discussed by Diaconis 1988. Cohen and Mallows 1980 propose graphical methods based on multi-dimensional scaling and biplots. Cohen 1990 presents alternate exploratory data techniques for ranked data.
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