Metric Methods for Analyzing Partially Ranked Data

Download or read book Metric Methods for Analyzing Partially Ranked Data written by Douglas E. Critchlow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: A full ranking of n items is simply an ordering of all these items, of the form: first choice, second choice, •. . , n-th choice. If two judges each rank the same n items, statisticians have used various metrics to measure the closeness of the two rankings, including Ken dall's tau, Spearman's rho, Spearman's footrule, Ulam's metric, Hal1l11ing distance, and Cayley distance. These metrics have been em ployed in many contexts, in many applied statistical and scientific problems. Thi s monograph presents genera 1 methods for extendi ng these metri cs to partially ranked data. Here "partially ranked data" refers, for instance, to the situation in which there are n distinct items, but each judge specifies only his first through k-th choices, where k