Intergroup diversity and concordance for ranking data: An approach via metrics for permutations. (English) Zbl 0604.62042

Feigin, Paul D.; Alvo, Mayer

Ann. Stat. 14, 691-707 (1986).

Motivated by the apportionment of diversity analysis due to C. R. Rao [see e.g., Theor. Popul. Biol. 21, 24-43 (1982; Zbl 0516.92021)], a general approach to comparing populations of rankers is proposed. Each permutation metric corresponds to a particular population characteristic that forms the basis of the comparison. Tests of hypotheses concerning equality of characteristics are developed.
Throughout, comparison is made with earlier work, most of which is based on the use of only the Spearman metric. Extension to tied rankings is discussed. Examples for two groups are presented which illustrate the computational feasibility as well as the value of the proposed procedures.

MSC:

62G99	Nonparametric inference
62G10	Nonparametric hypothesis testing
62G05	Nonparametric estimation
62H20	Measures of association (correlation, canonical correlation, etc.)

Keywords:

intergroup diversity and concordance; ranking data; Kendall’s tau; apportionment of diversity; comparing populations of rankers; permutation metric; Spearman metric; tied rankings

Citations:

Zbl 0516.92021