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Nonparametric Tests in the Unbalanced Multivariate One‐Way Design
Author(s) -
Munzel Ullrich,
Brunner Edgar
Publication year - 2000
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 - 10.1002/1521-4036(200011)42:7<837::aid-bimj837>3.0.co;2-s
Subject(s) - mathematics , nonparametric statistics , estimator , statistics , test statistic , wald test , statistic , multivariate statistics , asymptotic distribution , statistical hypothesis testing , econometrics
A nonparametric model for the multivariate one‐way design is discussed which entails continuous as well as discontinuous distributions and, therefore, allows for ordinal data. Nonparametric hypotheses are formulated by the normalized version of the marginal distribution functions as well as the common distribution functions. The differences between the distribution functions are described by means of the so‐called relative treatment effects, for which unbiased and consistent estimators are derived. The asymptotic distribution of the vector of the effect estimators is derived and under the marignal hypothesis a consistent estimator for the asymptotic covariance matrix is given. Nonparametric versions of the Wald‐type statistic, the ANOVA‐type statistic and the Lawley‐Hotelling statistic are considered and compared by means of a simulation study. Finally, these tests are applied to a psychiatric clinical trial.