Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation

This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges.