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Neighbor balance and evenness of distribution of treatment replications in row‐column designs
Author(s) -
Piepho HansPeter,
Michel Volker,
Williams Emlyn
Publication year - 2018
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201800013
Subject(s) - species evenness , row and column spaces , row , mathematics , replication (statistics) , column (typography) , statistics , computer science , algorithm , geometry , paleontology , connection (principal bundle) , database , species richness , biology
Row‐column designs allow error control in field experiments by blocking in two dimensions. While this strategy can capture spatial heterogeneity aligned with blocks and account for effects due to the farming operations along rows and columns, it suffers from the occasional clustered occurrence of several replications of the same treatment. This property of classical row‐column designs has hampered their more widespread use in practice. A further issue of practical importance is the degree of neighbor balance of a design, that is, the frequency of adjacencies of pairs of treatments. This paper proposes two design strategies to simultaneously optimize the evenness of spatial distribution of treatment replication as well as neighbor balance. Three examples are given to illustrate the proposed methods and demonstrate that both approaches yield comparable and satisfactory results.