Downloaded from https://www.everyspec.com AMCP 7WIS.1' 4. The general variable is xJ 1 ,; x 11 . means an Eq. 2-50 uses the fact that thm cross pro- average (in cell 1, ) cer all replications; ducts vanish due to wise choice of expres- •..means the average over everything and dlons in the ( ;this will be trute in all cases. 'Mbe allocation of sums of squares and 2-7.2 CASE h 1 FACTOR, WITH REPLI- degrees of freedom is most easily visualized CATION, TABLE 2-15 in a table. This case is shown In Table 2.16(A). The residuals estimate of the x 1 p Is the variable. It s subdivided U variance is used a a reference; It would shown in Eq. 2-49.
give the common within-factor variance even is zero by dcflnition (see x). if the factors were causing a shift in the x -r . 0 ) + (Xlr - -'Ti) (2-49) means. The ratio arl/s Is tested by means of the F statistic-the distribution of the Each of the terms in ( ) In Fq. 2-49 is used ratio of 2 a-Independent a from the sme to estimate the variance. population. If the ratio Is very high * + (rarely exceeded) It I doubtful that the s? 14 if . .)I me 2 u only the ommon varlanoe; there (2-50) Is very probably a real difference in the means. TABLE 2.16 Example No. 12 illustrates the case of one factor with replication. CANIMI 1:
1 FACTOR, WITH REPLICATION T.e data in Table 2-15(B) were actually (A) GENERAL CAN all taken from the table of standard s- normal random deviates (zero mean, unit F e variance) in Ref. 25 (p. 396). If we had found 1 2 ... I SRelkcatin 1 x x xTABLE 2.16 2 x x X 3 x x . ALLOCATION OF SUMS OF SQUARE$ AND DEGREES OF FREEDOM (A) ,wibim OW a1n1sMu•d fIN am I Dll (es T'he UmM m I mid o be are). (I) EXAMPLE, 1 FACTOR, 2 LEVELS, .. .. 4 REPLICATIONS *Poi , 2.96 -0.47 0,04 JI) Iitable Wo On*0 1-,, R- 4 I I1 1r EIE,txk- A,.)' Ithl- I, Sa+/u' - Lest: 1 2 3 .ta sY.,x'It - - - -0.39 1.24 -0.59 AINaUdOw as s o Fp -0.01 -0.40 -0.51 ..
..- -0.23 -1.69 0.03 1 2.0041 2 1.0424 0.7572 1 2.304 9 1,370le Mean 0.581 -0.330 -0.258 Tout 14.4)06 11 - " 'IN Entries idjusted wo that gram' waqer Is zro. (The total does not io wit 13, + 0ie bluaw of nqjoff urnoiw 241