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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-1,
author = {Wiktor Oktaba},
title = {Note on the ANOVA of a completely confounded factorial experiment},
journal = {Applicationes Mathematicae},
volume = {32},
year = {2005},
pages = {119-132},
zbl = {1075.62064},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-1}
}
Wiktor Oktaba. Note on the ANOVA of a completely confounded factorial experiment. Applicationes Mathematicae, Tome 32 (2005) pp. 119-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-1/