Geodesic
Note on the ANOVA of a completely confounded factorial experiment
Wiktor Oktaba1
1 Department of Mathematical Statistics Institute of Applied Mathematics Agricultural University Akademicka 13 20-934 Lublin, Poland
Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 119-132 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 a factorial experiment with completely confounded interaction is given. The treatment effect estimators and some relations between the matrix $\textbf{F}$ of the reduced normal equations and the information matrix $\textbf{A}$ are given. Moreover the ANOVA of the sum of squares for adjusted treatment effects and the matrix $\textbf{F}$ 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 $\textbf{F}$ is introduced (Theorems 3.2.1–3.2.4). The corresponding numerical example has been worked out by Oktaba (1956) and Oktaba, Rejmak and Warteresiewicz (1956) by applying Galois fields and congruences.
DOI : 10.4064/am32-2-1
Keywords: purpose paper present modern approach analysis variance anova disconnected resolvable group divisible partially balanced incomplete block gdpbib designs factorial structure interaction effects completely confounded characterization factorial experiment completely confounded interaction given treatment effect estimators relations between matrix textbf reduced normal equations information matrix textbf given moreover anova sum squares adjusted treatment effects matrix textbf its eigenvalues orthonormal eigenvectors completely confounded factorial experiment presented special form generalized inverse g inverse textbf introduced theorems corresponding numerical example has worked out oktaba oktaba rejmak warteresiewicz applying galois fields congruences

Wiktor Oktaba 1

1 Department of Mathematical Statistics Institute of Applied Mathematics Agricultural University Akademicka 13 20-934 Lublin, Poland 
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Wiktor Oktaba. Note on the ANOVA of a completely
 confounded factorial experiment. Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 119-132. doi: 10.4064/am32-2-1

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