Downloaded from https://www.everyspec.com AMCP 708-IN TABLE 2.18 CASE I1: ANALYSIS VARIANCE. 2 PACTORS, WITHOUT REPLICATION IA) Calculation and AIlowilons (The overall man ,.. Is resumed to be tero,) Alilwatle" U a F I ,/ - I ss Is/i ,;/, Total EZL(MIt)• IJ- 1 - w eiI linlples an Intaeaction toin,. (B) Experimental Layout to m epw ' to an exporiment. Factor I I _x _ , , x Factor 2 x .. N J .x. N Xtjk ( TO.. + .f.)( . T ) (r.,) averages must be subtracted from It; in the + aend, the Identity must also be preserved, + •.Ls " "..,) a. The first 3 terms have no further averages because ,. , 0 (by hypothesis; + (XIra - Neat.
- Yt.d) if not, I , , is subtracted from every + - 't , "" ., " ,.) reading). - ( 1t4.j. "a*. " .t.) b, Consider the first 2-way interaction, -see ~ "'.* 1*:.0 "' Its) 7The i•/ . ha& 2 further averages x . . and x.,.; each must be subtracted from xn , - (Mo..) - (V.,.) - (T.o.)) (2-54) But the i., . and э.,, have no further (non- zero) averages because 0. . . 0. The same The fOrst 3 terms give the main effects due considettkicng hold for the other 2-way to the 3 factors; the second 3 terms dlve the interactions, 2-way interaction effects; and the last term in [ J gives the 3-way interaction term, c, The 3-way interaction term begins with The i . t. . i written out in detail to hw :sii*.
It has 3 furthor averages (over each how It is oonst•rcted; it can be simplified in of the indexb); each of those averages has appeRance somewhat as in Table 2-20(A). 2 further averages-ind just repeats the 2-wfay Whenever a term is written down, all further Interaction terms, so each of those Is sub- S2-86'-