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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-1-4,
author = {Czes\l aw St\k epniak},
title = {Characterizing experimental designs by properties of the standard quadratic forms of observations},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {39-45},
zbl = {1112.62049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-1-4}
}
Czesław Stępniak. Characterizing experimental designs by properties of the standard quadratic forms of observations. Applicationes Mathematicae, Tome 34 (2007) pp. 39-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-1-4/