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A Nonparametric Test for Differences in the Dispersion of Dependent Samples
Author(s) -
Boehnke K.
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310403
Subject(s) - mathematics , statistic , nonparametric statistics , statistics , test statistic , completeness (order theory) , rank (graph theory) , sufficient statistic , statistical hypothesis testing , dispersion (optics) , distribution (mathematics) , combinatorics , mathematical analysis , physics , optics
A new statistic Δ to test the hypothesis of a difference in the dispersion of two dependent samples of ordinal data quality is proposed. It draws on the idea of rank assignment originally forwarded by Siegel and Tukey (1960). No exact probability levels can be given for this statistic for the time being, but it is shown that the statistic is linearly related to the so‐called Hotelling‐Pabst statistic D , and that one can use exact tables of the latter as a substitute in the statistical decision process with small samples. For larger samples, an approximation of Δ to the standard normal distribution is given. The problem of tied observations is not sufficiently solved yet. A conservative procedure of rank assignment is proposed as long as the exact distribution of Δ in the presence of ties is unknown.