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Note on the ANOVA of a completely confounded factorial experiment. (English) Zbl 1075.62064

Summary: The purpose of this paper is to present a modern approach to the analysis of variance (ANOVA) of disconnected resolvable group divisible partially balanced incomplete block (GDPBIB) designs with factorial structure and with some interaction effects completely confounded. A characterization of factorial experiments with completely confounded interactions is given. The treatment effect estimators and some relations between the matrix F of the reduced normal equations and the information matrix A are given.
Moreover the ANOVA of the sum of squares for adjusted treatment effects and the matrix F with its eigenvalues and orthonormal eigenvectors for the case of a completely confounded factorial experiment are presented. A special form of a generalized inverse (\(g\)-inverse) of F is introduced. The corresponding numerical example has been worked out by W. Oktaba [Ann. Univ. Mariae Curie-Skłodowska 11, 123–186 (Polish) (1956)] and W. Oktaba, W. Rejmak and M. Warteresiewicz [ibid., 187–226 (Polish) (1956)] by applying Galois fields and congruences.

MSC:

62K15 Factorial statistical designs
62J10 Analysis of variance and covariance (ANOVA)
15A18 Eigenvalues, singular values, and eigenvectors
62K10 Statistical block designs
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