Note on the ANOVA of a completely confounded factorial experiment

Wiktor Oktaba. "Note on the ANOVA of a completely confounded factorial experiment." Applicationes Mathematicae 32.2 (2005): 119-132. <http://eudml.org/doc/279387>.

@article{WiktorOktaba2005,
abstract = {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.},
author = {Wiktor Oktaba},
journal = {Applicationes Mathematicae},
keywords = {disconnected orthogonal block design; completely confounded design; reduced normal equations; PBIB; Group Divisible (GD); F matrix; Galois field; congruence; ANOVA; graphical method “O”},
language = {eng},
number = {2},
pages = {119-132},
title = {Note on the ANOVA of a completely confounded factorial experiment},
url = {http://eudml.org/doc/279387},
volume = {32},
year = {2005},
}

TY - JOUR
AU - Wiktor Oktaba
TI - Note on the ANOVA of a completely confounded factorial experiment
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 2
SP - 119
EP - 132
AB - 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.
LA - eng
KW - disconnected orthogonal block design; completely confounded design; reduced normal equations; PBIB; Group Divisible (GD); F matrix; Galois field; congruence; ANOVA; graphical method “O”
UR - http://eudml.org/doc/279387
ER -