Abstract
This paper gives a general method for constructing quasi-Latin square, quasi-Latin rectangle and extended quasi-Latin rectangle designs for symmetric factorial experiments. Two further methods are given for parameter values satisfying certain conditions. The construction of designs for a range of numbers of rows and columns is discussed so that the different construction techniques are covered. For some row and column combinations, different designs are compared. The construction of designs with rows and columns that are nested or contiguous is also discussed.
Highlights
Our aim is to produce designs with rows and columns for a factorial set of treatments
The quasi-Latin rectangle designs increase the range of situations in which factorial treatments can be assigned in a row-column design with orthogonal factorial structure
Our objective is not to obtain the “best design” for a given set of factorial treatments and of units, but to give several competing designs each of which is applicable in different circumstances; see for example Section 6.2
Summary
Our aim is to produce designs with rows and columns for a factorial set of treatments. The designs have at least two factors, Rows and Columns, indexing the experimental units, and allow for the removal, from error variance, of at least the two corresponding sources of variation. In one experiment described in [16], a design was required for an experiment to investigate the effects of five treatment factors on the growth of species of Australian native plants that potentially could be used in the remediation of sites in the rail corridor either side of railway tracks. Three of the factors each had two levels and the resulting eight treatments were to be applied to main plots that were arranged in a 4 × 10 rectangle. A design for the main plot treatments is required
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