Listy Biometryczne - Biometrical Letters Vol. 37(2000), No. 2, 97-105
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ORTHOGONAL CONTRASTS FOR RANK ONE COMMON STRUCTURES
M.M. Oliveira1, J.T. Mexia2 1Departameiito de Matematica, Universidade de Evora, Colégio Luis Antonio Verney, Rua Romao Ramăo 59. 7000 Évora, Portugal 2Departamento de Matematica, Universidade Nova de Lisboa, Faculdade de Ciencias e Tecnologia, Quinta da Torre, 2825 Monte da Caparica, Portugal |
The relations between studies in a series, when STATIS (Structuration des Tableaux a Trois Indices de la Statistique) or Dual STATIS is applied, are expressed by the Hilbert-Schmidt products of the operators associated to those studies. Studies in a series are said to have a common structure whenever the matrix of Hilbert-Schmidt products is the sum of a rank one matrix with an error matrix. When such a common structure exists, the components of the structure vector will suffice to locate the studies in the series. Assuming that for all level combinations of L factors there are matched series of studies presenting common structures, standardized orthogonal matrices are used to analyze the influence of those factors on the corresponding structure vectors.
STATIS, Dual STATIS, Hilbert-Schmidt products, structure vectors, F tests, orthogonal contrasts, standardized orthogonal matrices.
