Open Access
Translator Disclaimer
December, 1965 The Relationship Algebra and the Analysis of Variance of a Partially Balanced Incomplete Block Design
Junjiro Ogawa, Goro Ishii
Ann. Math. Statist. 36(6): 1815-1828 (December, 1965). DOI: 10.1214/aoms/1177699811

Abstract

The analysis of variance of a partially balanced incomplete block design is investigated in connection with its relationship algebra. This gives a somewhat clearer insight into the structure of the partition of the total sum of squares than before. A. T. James [5] dealt with the same problem with the balanced incomplete block design and this article should be regarded as a generalization of his work to the partially balanced incomplete block design. The definitions and necessary notations concerning a partially balanced incomplete block design (PBIBD) and its association algebra are briefly given in Section 1. Although the properties of the association algebra have been known in another expression [4], they are presented in Section 2 in the form fitting to our discussions on the relationship algebra. In Section 3, the definition and properties of the relationship algebra of a PBIBD are given and these are believed to be new. In Section 4, the analysis of variance of a PBIBD is considered and the partition of the sum of squares due to treatments adjusted pertinent to the association under consideration is given. Finally, Section 5 is devoted to the analysis of variance of a PBIBD of triangular type and a numerical illustration.

Citation

Download Citation

Junjiro Ogawa. Goro Ishii. "The Relationship Algebra and the Analysis of Variance of a Partially Balanced Incomplete Block Design." Ann. Math. Statist. 36 (6) 1815 - 1828, December, 1965. https://doi.org/10.1214/aoms/1177699811

Information

Published: December, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0136.40705
MathSciNet: MR189191
Digital Object Identifier: 10.1214/aoms/1177699811

Rights: Copyright © 1965 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.36 • No. 6 • December, 1965
Back to Top