GRCdesigns: Generalized Row-Column Designs

Abstract

When the number of treatments is large with limited experimental resources then Row-Column(RC) designs with multiple units per cell can be used. These designs are called Generalized Row-Column (GRC) designs and are defined as designs with v treatments in p rows and q columns such that the intersection of each row and column (cell) consists of k experimental units. For example (Bailey & Monod (2001)<doi:10.1111/1467-9469.00235>), to conduct an experiment for comparing 4 treatments using 4 plants with leaves at 2 different heights row-column design with two units per cell can be used. A GRC design is said to be structurally complete if corresponding to the intersection of each row and column, there appears at least two treatments. A GRC design is said to be structurally incomplete if corresponding to the intersection of any row and column, there is at least one cell which does not contain any treatment. Function SCGRC_I, SCGRC_II, SCGRC_III generates three series of structurally complete GRC designs and SIGRC_I, SCGRC_II generates two series of Structurally incomplete GRC designs.