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AN ASYMPTOTICALLY DISTRIBUTION‐FREE MULTIPLE COMPARISON METHOD WITH APPLICATION TO THE PROBLEM OF n RANKINGS OF m OBJECTS
Author(s) -
Rosenthal Irene,
Ferguson Thomas S.
Publication year - 1965
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1965.tb00344.x
Subject(s) - mathematics , ellipsoid , rank (graph theory) , asymptotically optimal algorithm , statistic , statistics , distribution (mathematics) , population , sample (material) , combinatorics , joint probability distribution , test statistic , order statistic , statistical hypothesis testing , mathematical optimization , mathematical analysis , demography , physics , chemistry , chromatography , astronomy , sociology
The statistic known as Hotelling's T 2 is shown to be asymptotically distribution‐free and thus to provide a multi‐dimensional confidence ellipsoid for the joint population means which enables multiple comparisons of sample means to be made. If m objects are ranked in order by each of n judges, Friedman's test is usually used to test the hypothesis that the judges rank the objects at random. It is of interest, however, to enquire which of the objects are ranked significantly higher than others, in which case Hotelling's T 2 may be used to provide asymptotically distribution‐free multiple comparisons.