Characterizing experimental designs by properties of the standard quadratic forms of observations

@article{CzesławStępniak2007,
abstract = {For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.},
author = {Czesław Stępniak},
journal = {Applicationes Mathematicae},
keywords = {2-way classification; standard quadratic forms; independence; nonnegative definiteness; characterization of designs},
language = {eng},
number = {1},
pages = {39-45},
title = {Characterizing experimental designs by properties of the standard quadratic forms of observations},
url = {http://eudml.org/doc/279218},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Czesław Stępniak
TI - Characterizing experimental designs by properties of the standard quadratic forms of observations
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 1
SP - 39
EP - 45
AB - For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.
LA - eng
KW - 2-way classification; standard quadratic forms; independence; nonnegative definiteness; characterization of designs
UR - http://eudml.org/doc/279218
ER -