Optimal a\(\times b\) connected designs with \(a+b\) observations
In an experiment to investigate the effect of factor 1, with a levels, and factor 2, with b levels, on a response variable Y, suppose that only n observations can be afforded, where n is a small number such as \(a+b-1\) or \(a+b\). The problem of determining the best design for placing these n observations is here considered under the usual two-factor model without interaction. The designs constructed by placing a observations at a single level of factor 2 and b observations at a single level of factor 1 will be said to be perpendicular. For the problem of determining optimal \(a\times b\) two-factor designs with only \(a+b\) observations, the present paper shows that, when \(a\neq 3\), the A-optimal designs are those constructed by placing \(a+b-1\) observations in a perpendicular pattern so that a observations are at a single level of factor 2 and b observations are at a single level of factor 1, and then adding one more observation. These designs are also optimal under a modification of the E-criterion.
scientific article; zbMATH DE number 4211309