Orthogonality of factorial effects. (English) Zbl 0655.62080

Chauhan, Chand K.; Dean, A. M.

Ann. Stat. 14, 743-752 (1986).

Summary: A necessary and sufficient condition is given for a specified factorial effect to be orthogonal to every other factorial effect, after adjustment is made for blocks. The results are extended to the case of regular disconnected designs. The structure of a generalized inverse of the intrablock matrix is investigated when certain pairs of factorial spaces are orthogonal. A useful class of designs exhibiting partial orthogonal factorial structure is identified and examples are given.

MSC:

62K15	Factorial statistical designs
62K10	Statistical block designs
15A09	Theory of matrix inversion and generalized inverses

Keywords:

incomplete block designs; factorial effect; adjustment; regular disconnected designs; generalized inverse of the intrablock matrix; partial orthogonal factorial structure