- 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 square s andLatin hypercube sampling

*Graeco-Latin square s**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

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Graeco-Latin square**— Orthogonal Latin squares of order 3 Orthogonal Latin squares of order 5 In mathematics, a Graeco Latin square or Euler square or orthogonal Latin squares of order n over two … Wikipedia**Latin hypercube sampling**— (LHS) is a statistical method for generating a distribution of plausible collections of parameter values from a multidimensional distribution. The sampling method is often applied in uncertainty analysis. The technique was first described by… … Wikipedia**Design of experiments**— In general usage, design of experiments (DOE) or experimental design is the design of any information gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms… … Wikipedia**Randomized block design**— In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to … Wikipedia**Combinatorial design**— theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties. For instance, a balanced incomplete block design (usually called for … Wikipedia**Optimal design**— This article is about the topic in the design of experiments. For the topic in optimal control theory, see shape optimization. Gustav Elfving developed the optimal design of experiments, and so minimized surveyors need for theodolite measurements … Wikipedia**Bayesian experimental design**— provides a general probability theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. This allows accounting for… … Wikipedia**Completely randomized design**— In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one… … Wikipedia**List of statistics topics**— Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… … Wikipedia**List of mathematics articles (H)**— NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… … Wikipedia