Note on the ANOVA of a completely confounded factorial experiment

• Autorzy: Wiktor Oktaba
• Języki publikacji: EN

Abstrakty

EN

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 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 (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.

Kategorie tematyczne

• 62K10: Block designs
• 62K15: Factorial designs

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2005
• Tom: 32
• Numer: 2
• Strony: 119-132

Daty

wydano

2005

Twórcy

autor

Wiktor Oktaba

• Department of Mathematical Statistics, Institute of Applied Mathematics, Agricultural University, Akademicka 13, 20-934 Lublin, Poland

Identyfikatory

DOI

10.4064/am32-2-1