# X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Biometrical Letters (2015)

- Volume: 52, Issue: 1, page 1-12
- ISSN: 1896-3811

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topRyszard Walkowiak. " X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs ." Biometrical Letters 52.1 (2015): 1-12. <http://eudml.org/doc/270971>.

@article{RyszardWalkowiak2015,

abstract = {This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity h−1, where h is the rank of the matrix C. It was found that for each such design there exists a diagonal positive definite matrix X such that the design is X −1-balanced.},

author = {Ryszard Walkowiak},

journal = {Biometrical Letters},

keywords = {block design; row-column design; efficiency balance; variance balance; X−1-balance},

language = {eng},

number = {1},

pages = {1-12},

title = { X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs },

url = {http://eudml.org/doc/270971},

volume = {52},

year = {2015},

}

TY - JOUR

AU - Ryszard Walkowiak

TI - X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

JO - Biometrical Letters

PY - 2015

VL - 52

IS - 1

SP - 1

EP - 12

AB - This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity h−1, where h is the rank of the matrix C. It was found that for each such design there exists a diagonal positive definite matrix X such that the design is X −1-balanced.

LA - eng

KW - block design; row-column design; efficiency balance; variance balance; X−1-balance

UR - http://eudml.org/doc/270971

ER -

## References

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- Pearce S.C. (1960): Supplemented balance. Biometrica 47(3&4): 263-271.[Crossref] Zbl0104.37203
- Pearce S.C. (1975): Row and column designs. Appl. Statist. 24: 60-74.
- Pearce S. C., Caliński T., Marshall T. F. de C. (1974): The basic contrasts of an experimental designs with special reference to the analysis of data. Biometrika 61: 449-460.[Crossref] Zbl0292.62052
- Raghavarao O., Federer W.T. (1975): On connectedness in two-way elimination of heterogeneity designs. Ann. Statist. 3: 730-735. Zbl0303.62063
- Rao C.R., Mitra S.K. (1971): Generalized inverse of matrices and its applications. New York, Wiley. Zbl0236.15004

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