Important properties of an experimental design, including the analysis of variance appropriate to it, are revealed by analysing the structure of an algebra generated by the relationships between the experimental units of the design. As an illustration, the relationship algebra of balanced incomplete blocks is analysed in detail.
"The Relationship Algebra of an Experimental Design." Ann. Math. Statist. 28 (4) 993 - 1002, December, 1957. https://doi.org/10.1214/aoms/1177706800