Partitioning of interaction in analysis of variance

Abstract

A method is prese nted for th e analysis of data re prese ntin g fun c tion s of two variables , when the res pon se ca n be tabulate d in a rec tangular array.Th e procedure is based o n a partiti onin g of the row by column inte rac tion e ffe c ts into a s um of terms, eac h of which is th e produ c t of a row fac tor by a column fa c tor.The factors in eac h te rm a re est im a te d by a method involv ing th e ext rac ti on of c ha rac te ristic roots.Th e me thod co ntain s as s pec ial cases a number of proced ures used for th e handling of non•addi• tivity in tlVO way a rrays.It is ve ry use ful for th e fittin g of e mpiri ca l s urfaces, but is a lso appli ca ble to cases in wh ic h th e data d e pend on qu a lit a tive rat he r th a n qu an tita tive factors.Co mpariso ns with oth e r tec hniqu es are made a nd a n illu s tra ti ve exa mple is g iv e n.