The Analysis of Lattice Designs with Concomitant Variables Associated with Replications

Abstract

The analysis of lattice designs is extended to treatments each having a linear response to m X -variables associated with replications, m < pk /( k + 1) − 1, where p is the number of replications and k is the block size. The design is a split plot with subplot treatments arranged as a lattice design having main plots as the lattice replicates. Formulas are obtained for converting ordinary least squares estimates of treatment regression coefficients into weighted least squares estimates, and for the covariance matrix of a difference between corrected treatment regression coefficient vectors. The general theory allows for repetition (not necessarily equal) of the basic patterns of confounding treatments with blocks.