To analyze the response variable, yield, we need to identify the two basic components of the experiment: the treatment structure and the blocking (or design) structure. Analysis of a balanced lattice square design The Row and Column factors define the row and column positions within the field (rather than within each replicate). That is, within each replicates the lattice rows ( RowRep) and lattice columns ( ColRep) are both numbered from 1 to 5. The lattice block numbering is coded within replicates. The six replicates are numbered from 1 to 6 ( Rep). There are seven columns in the data frame: five blocking factors ( Rep, RowRep, ColRep, Row, Column), one treatment factor, Variety, and the response variate, yield. The variety grown in each plot, and the coding of the replicates and lattice blocks, is shown in the field layout below: Each replicate contained exactly one plot for every variety. The experiment was set up to compare the performance of 25 varieties of barley and was designed as a balanced lattice square with six replicates laid out in a 10 x 15 rectangular grid. The example data are from a field experiment conducted at Slate Hall Farm, UK, in 1976 (Gilmour et al., 1995).
We’ll consider two models: the balanced lattice square model and a spatial model.
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This blog illustrates how to analyze data from a field experiment with a balanced lattice square design using linear mixed models.