Efficient semi-Latin rectangles: designs for plant disease experiments (Q2739863)

A semi-Latin rectangle is a row-column design in which: (i) each row-column intersection has the same size \(k>1\); (ii) every treatment occurs the same number of times in each row; (iii) every treatment occurs the same number of times in each column.NEWLINENEWLINENEWLINEThe authors consider mainly the case of \(n\) rows and \(2n\) columns. In this case \(k=2\) and the number of treatments is \(2n\). Methods of semi-Latin rectangles construction are described for the case. Harmonic-mean efficiency factors and variances of the corresponding estimators are calculated. It is noted that the presented designs are E-optimal for \(n\geq 3\), A-optimal for \(n=3,4\) and D-optimal for \(3\leq n\leq 7\). An application to the analysis of plant leaves desease is considered.