# Hyper-Graeco-Latin square design

- Hyper-Graeco-Latin square design
In the design of experiments, **hyper-Graeco-Latin squares** are efficient designs to study the effect of one primary (treatment) factor in the presence of 4 blocking (nuisance) factors. They are restricted, however, to the case in which all the factors have the same number of levels.

Designs for 4- and 5-level factors are given in this article. These designs show what the treatment combinations should be for each run. When using any of these designs, the treatment units and trial order should be randomized as much as the design allows. For example, one recommendation is that a hyper-Graeco-Latin square design be randomly selected from those available, then randomize the run order.

There are no 3-level factor hyper-Graeco Latin square designs.

**Design for 4-level factors**

For 4-level factors, the design consists of sixteen runs:This can alternatively be represented as (A, B, C, D, and E represent the treatment factor and 1, 2, 3, 4, and 5 represent the blocking factors):

**ee also**

* Latin squares and Latin hypercube sampling

* Graeco-Latin squares

**External links**

* [*http://www.itl.nist.gov/div898/handbook/pri/section3/pri3323.htm Hyper-Graeco-Latin square designs*]

* [*http://support.sas.com/documentation/cdl/en/qcug/59658/HTML/default/fac_details_sect23.htm A SAS example using PROC FACTEX*]

**References**

*cite book |names=Box, G. E. P., Hunter, W. G., and Hunter, J. S.| year=1978|title=Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building|publisher=John Wiley and Sons

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