Download presentation

Presentation is loading. Please wait.

Published byMarlene Norfleet Modified over 2 years ago

1
Figure 7 Fractional Factorials This first example (C=AB) is in the book c1 c2 a1b1 b2 a2b1 b2 ConditionGMABCABACBCABC a 1 b 1 c 1 1-1-1-1 1 1 1-1 a 1 b 1 c 2 1-1-1 1 1-1-1 1 a 1 b 2 c 1 1-1 1-1-1 1-1 1 a 1 b 2 c 2 1-1 1 1-1-1 1-1 a 2 b 1 c 1 1 1-1-1-1-1 1 1 a 2 b 1 c 2 1 1-1 1-1 1-1-1 a 2 b 2 c 1 1 1 1-1 1-1-1-1 a 2 b 2 c 2 1 1 1 1 1 1 1 1 ConditionGMABCABACBCABC a 1 b 1 c 2 1-1-1 1 1-1-1 1 a 1 b 2 c 1 1-1 1-1-1 1-1 1 a 2 b 1 c 1 1 1-1-1-1-1 1 1 a 2 b 2 c 2 1 1 1 1 1 1 1 1

2
Figure 7, continued "confounding" or "aliases": start with confounding grand mean and highest order interaction effect in full 2 3 in 1/2 2 3 where GM = ABC GMGM = ABC AA(ABC) = A 2 BC = BCA & BC are aliases BB(ABC) = AB 2 C = ACB & AC are aliases CC(ABC) = ABC 2 = ABC & AB are aliases ABAB(ABC) = A 2 B 2 C = C ACAC(ABC) = A 2 BC 2 = B BCBC(ABC) = AB 2 C 2 = A ABCABC(ABC) = A 2 B 2 C 2 = GM This first example (C=AB) is in the book

3
Figure 8 Fractional Factorial: Planning ConditionGMABCABACBCABC a 1 b 1 c 1 1-1-1-1 1 1 1-1 a 1 b 2 c 1 1-1 1-1-1 1-1 1 a 2 b 1 c 2 1 1-1 1-1 1-1-1 a 2 b 2 c 2 1 1 1 1 1 1 1 1 c1 c2 a1b1 b2 a2b1 b2 GMAC GM & AC are aliases AA(AC) = A 2 C = CA & C are aliases BB(AC) = ABC = ABCB & ABC are aliases CC(AC) = AC 2 = A ABAB(AC) = A 2 BC = BCAB & BC are aliases ACAC(AC) = A 2 C 2 = GM BCBC(AC) = ABC 2 = AB ABCABC(AC) = A 2 BC 2 = B

4
so ANOVA table:sourcedf A (or BC)1 B (or AC)1 C (or AB)1 need error term need to assume higher order interactions are not significant or interesting Fractional Factorials

5
2nd ex/ 2 4 factorial, fraction confound GM = ABCD Source in 2 4 in fractional factorial AA(ABCD) = A 2 BCD = BCD BB(ABCD) = AB 2 CD = ACD CABC 2 D = ABD DABCD 2 = ABC ABA 2 B 2 CD = CD ACA 2 BC 2 D = BD ADA 2 BCD 2 = BC BCAB 2 C 2 D = AD BDAB 2 CD 2 = AC CDABC 2 D 2 = AB ABCA 2 B 2 C 2 D = D ABDA 2 B 2 CD 2 = C ACDA 2 BC 2 D 2 = B BCD AB 2 C 2 D 2 = A ABCDGM Fractional Factorials So, assuming you expect main effects A,B,C, & D, couldn't untangle them from BCD, ACD, ABD, ABC. Furthermore, aliasing/confounding of AB = CD, AC = BD, AD = BC. Clearly if you expect some higher-order interactions, better think hard before using this design. (used in conjoint…)

Similar presentations

Presentation is loading. Please wait....

OK

Properties from Algebra

Properties from Algebra

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on series and parallel circuits pdf Ppt on diode circuits problems Free ppt on moving coil galvanometer to ammeter Ppt on responsive web design Ppt on brand building strategy Ppt on content development manager Ppt on septic abortion Ppt on spirit of unity in india Ppt on asymptotic notation of algorithms to solve Ppt on ram and rom hyper