Oktaba, Wiktor Note on the ANOVA of a completely confounded factorial experiment. (English) Zbl 1075.62064 Appl. Math. 32, No. 2, 119-132 (2005). 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 Keywords:disconnected orthogonal block design; completely confounded design; reduced normal equations; PBIB; Group Divisible (GD); F matrix; Galois field; congruence; ANOVA; graphical method “O” PDFBibTeX XMLCite \textit{W. Oktaba}, Appl. Math. 32, No. 2, 119--132 (2005; Zbl 1075.62064) Full Text: DOI