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Non‐Parametric Methods for the 2‐Period‐Cross‐Over Design Under Weak Model Assumptions
Author(s) -
Brunner E.,
Neumann N.
Publication year - 1987
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.4710290804
Subject(s) - nonparametric statistics , equivalence (formal languages) , mathematics , rank (graph theory) , parametric statistics , parametric model , statistics , linear model , invariant (physics) , period (music) , econometrics , discrete mathematics , combinatorics , physics , acoustics , mathematical physics
A nonparametric analysis for the two period cross‐over design has first been suggested by Koch (1972) and has been discussed by Hills and Armitage (1979). As known rank tests on sums or differences of the data are applied in this procedure, the results on the one hand are not invariant under monotonous transformations and on the other hand the procedure is only correct for models with additive effects. Therefore, in the present article generalized effects will first be defined in the 2‐period cross‐over design without the assumption of a linear model and then rank test will be presented which test tese effects without the need of sums or differences of the data. In the appendix the equivalence of the hypothesis for the generalized effects to the known hypotheses for the effects in the linear model will be shown. The application of the procedures will be demonstrated by means of an example in literature.