A method is presented for the statistical analysis of sets of data which are assembled from multiple experiments. The analysis recognizes the existence of both within group and between group variabilities, and calculates appropriate weighting factors based on the observed variability for each group. The weighting factors are used to calculate a "best" consensus value from the overall experiment. The technique for obtaining the consensus value is applicable to either the determination of the weighted average value, or to the parameters associated with a weighted least squares regression problem. The calculations are made by using an iterative technique with a truncated Taylor series expansion. The calculations are straightforward, and are easily programmed on a desktop computer.An examination of the observed variabilities, both within groups and between groups, leads to considerable insight into the overall experiment and greatly aids in the design of future experiments.

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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.Key words: Fac torial Experiments; inte rac ti on; nonadditivit y; prin c ip al co mpone nt s; s urface fittin g.