The Exact Analysis of Augmented Incomplete Latin Square Design with One Missing Observation

As Federer's augmented Latin square design (ALSD) is one of the most important augmented designs used in plant breeding programs, this paper aims to introduce an exact analysis for an ALSD with a missing check treatment. Namely, the novelty of this present work is evident in proposing and defining the augmented incomplete Latin square design (AILSD). In this light, the effects of rows, columns, checks, and new treatments were evaluated. All previous known studies were limited by focusing on dealing with complete datasets, paying less attention to the problem of the presence of a missing value, and this is the gap we are trying to fill here. Moreover, computing the regression sum of squares (RSS) for both full and reduced models was essential to figure out the other needed sum of squares. A numerical example and R simulation study were carried out to assess the performance of the proposed design. The importance of employing R comes from filling the calculation gaps involved in analysing AILSD.