New Technique to design Graeco Latin square for odd numbers of treatments

  • Omiad Saber Abdullah Department of Statistics - College of Administration / Salahaddin University-Erbil
Keywords: Technique, design, Graeco, treatments


In any laboratory or field experiment, if homogeneity is provided on the experimental units, the Complete Random Design (CRD) is the best design, on the condition that the conditions (assumptions) for the analysis of variance (ANOVA) are available. If the homogeneity is not ensured, to control systematically one source of extraneous variability the Randomized Complete Block Design (RCBD) is the best. In the case of two sources of external variability, the Latin Square Design (LSD) design is best. If three sources of external variability are present, the Graeco Latin Square Design (GLSD) is better, but this design is complicated because of the two conditions available for the (GLSD) which is not to repeat letters for the rows and columns, and every letter must contain one Greek letter. In the case of 6*6 design, we do not feel able to do this. Therefore, I have found a new technique for all designs that have odd numbers of (n) treatments. This method can help researchers in their scientific research.


BOX, G. E., HUNTER, J. S. & HUNTER, W. G. 2005. Statistics for Experimenters: Design, Innovation, and Discovery, Wiley-Interscience New York.
COCHRAN, W. G. & COX, G. M. 1957. Experimental Designs, John wiley & Sons
COX, D. R. & REID, N. 2000. The theory of the design of experiments, Chapman and Hall/CRC.
MONTGOMERY, D. C. 2017. Design and analysis of experiments, John wiley & sons.
WINER, B. J. 1962. Statistical principles in experimental design, McGRAW-HILL BOOK COMPANY United States of America.
How to Cite
Abdullah O. New Technique to design Graeco Latin square for odd numbers of treatments. JAHS [Internet]. 15Feb.2019 [cited 18Aug.2019];23(1):190 -20. Available from: