Downloaded from https://www.everyspec.com AMCP 19 1 an effect, it would have been an erroneous Xj * (Ri.) + M1.j) + (x 1 - . - J) finding. (2-62) This is about the simplest possible case, There are several algebra identities for re- It can be shown that, as in Table 21 8(A), ducing the amount of arithmetic (see Rel'. the sums of cross products vanish. The 32, for example); their use may incur round- dirficulty with this cam (no replication) Is ing errors which can be severe. An example that there is presumed to be no Interaction; of rounding errors can be shown using the therefore: the s2 is taken us the reference identity for the I'-ratio lest.
'fable 2-18(B) shows graphically what tests ar run.a y,,(a+b)(a-b),a|-b' (2-1) . 2.7.4 CASE II": 2 FACTORS, WITH Suppose a - 100,003, b -. 100,002 and the REPLICATION, TABLE 2.19 computer has only 6 signifctant figures. If the factored formula is used, we have xy, Is the variable. It Is subdivided us thown in Eq. 2-53. (100,003 + 100,002) (100,003 - I00,002) * 200,005 X I - 200,005. xgj m (RI..) 0 +. .) 0 If the other formula I& used, we have 31 (lj . -- g., "1. j.) 100,0032 - 100,002 - I00,(W0 X 101 - + (Xjt, -. Vfj.) (2-58) 100,004 X 101 s "200,M00. It can be shown that, as In Table 2-19(A), The rounding error by the second method the sums of cross products vanish.
The first caused a toss of almust 1 significant digit. 2 ierms will give the main effects of the 2 factors I and J; the 3rd term &ives the Inter- Another advantage of not using "short action effect; and the last term gives the cut" methods Is that one has a chknce to estimate of the population varfiace from the se the residuals and to note any that may replication (this Is used as the reference for be anomalous. testing the other effects). Table 2-19(B) shows the experimental layout; there are Most analyses actually wili be done via a IJR experimeists to be run. Tlble 2-19(A) computor program.
Check your computer shows that there are 3 F-weit., If the s- sarvice center to fln out which ones are signlflcanve level is too loose, there Is a available to you. good chance that one of the 3 effrtw will be declared s-significant when the F-value 2-7.3 CASE Ih: 2 FACTORS, WITHOUT Is high Just duw to chance. REPLICATION, TABLE 2-16 iP 2-7.5 CASE IV: 3 FACTORS, WITHOUT It is usually a poor Idea to have no re- REPLICATION, TABLE 2.20 plication.
Without replication, one must resort to precarious assumptions to estimate As in Case 11, It is usually a poor idea to the reference for the population variance., have no replication; but the number of tests with replication can be prohtibitive, xilk is x# Is the variable. It is subdivided as the variable. It Is subdivided as shown In shown in Eq. 2-52(x,. .. 0). Eq. 2-54. (i.. -). 2.8 _,/+:++,~~azi I.... -5 :'