One Missing Value Problem in Latin Square Design of Any Order: Regression Sum of Squares

Abstract

This paper introduced an incomplete Latin square design that leads to difficulties in the analysis of variance (ANOVA). The aim was to determine the explicit and mathematical formulae for the regression sum of squares for the full model of experimental data by means of the exact approach. From an overall review of the literature, the gap was a lack of definite formula for the ANOVA table for the cases of the incomplete Latin square designs. However, in this paper, the least square normal equations for the one-missing-value Latin square design were built to determine the estimates of model parameters and the regression sum of squares of the full effect model. It is noted that the regression sum of squares of the full effect model is one part of the analysis of variance with the exact approach.