One Missing Observation in Graeco Latin Square Design: An Approximate Analysis of Variance
Author(s)
Kupolusi, Joseph A. , Ojo, Oluwadare O. ,
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Abstract
Background: Experimental results can seriously be affected by different degrees of variation that arise from unknown or uncontrollable design factors which is not of interested to the experimenter that may probably has effect on the response. Blocking is an extremely important design technique that can be used to systematically eliminate the effect of the uncontrollable design factors. Graeco-Latin Square design is used to eliminate three sources of variability; that is, it systematically allows blocking in three directions. Thus, rows, columns and Greek letters actually represent three restrictions on randomization. There are situations whereby one observation is occasionally missed in a Graeco Latin Square design of order P x P. In this paper, we proposed an approximate method for one missing observation in Graeco Latin Square Design of any order.
Results: The proposed approximate method was applied to a data set of Graeco Latin Square Design of order 4 and the results are presented in ANOVA tables. Based on this result, Mean Sum of Squares (MSE) reduced drastically compared to that of complete data set. Reduction in MSE is a clear indication that the proposed method can be used to obtain a better result with a minimum variance and unbiased estimate.
Conclusion: The result of the analysis indicated that the proposed approximate method for Graeco Latin Square is appropriate for estimation of missing observation through a simulation study of 1000 experimental runs. The result converged to the real data set. Hence, the method derived in this research is capable to handling the problem of missing observation in Graeco-Latin Square design.
Keywords
Latin Square, Graeco Latin Square, ANOVA, missing data, experimental error
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