this sample size reduction comes at a statistical power cost, rendering the estimation of some three-way interactions or higher-order interactions impossible. Therefore,
the advantages of the orthogonal design are: i) obtaining information of the effects of all the factors in a single experiment of moderate size; ii) enabling the analysis of the effect of one factor under varied conditions of others; and iii) facilitating the analysis of the two-way interactions,
which may be the most important reason to include more than one factor in an experiment