InterEffectOrthogonality in Factorial Experiments

A set of necessary and sufficient conditions has been established for best linear estimates of estimable treatment contrasts belonging to different facotrial effects to be mutually orthogonal. The cases of both connected and disconnected designs have been considered. The analysis of connected designs satisfying the orthogonality condition has been derived. The orthogonality condition obtained is seen to throw new light on some of the existing methods of construction of symmetric and asymmetric factorial designs. Extension of the conditions to designs eliminating heterogeneity in several directions is immediate