Homework13
Hossein Bahreinizad
Felipe Zambrini Santos
Last compiled on November 30, 2022 at 10:14 PM - CST
8.2
library(FrF2)
obs <- c(7.037, 16.867, 13.876, 17.273, 11.846, 4.368, 9.360, 15.653)
des <- FrF2(nfactors = 4,resolution = 4,randomize = FALSE)
des <- add.response(des,obs)
summary(des)## Call:
## FrF2(nfactors = 4, resolution = 4, randomize = FALSE)
##
## Experimental design of type FrF2
## 8 runs
##
## Factor settings (scale ends):
## A B C D
## 1 -1 -1 -1 -1
## 2 1 1 1 1
##
## Responses:
## [1] obs
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D
##
## $generators
## [1] D=ABC
##
##
## Alias structure:
## $fi2
## [1] AB=CD AC=BD AD=BC
##
##
## The design itself:
## A B C D obs
## 1 -1 -1 -1 -1 7.037
## 2 1 -1 -1 1 16.867
## 3 -1 1 -1 1 13.876
## 4 1 1 -1 -1 17.273
## 5 -1 -1 1 1 11.846
## 6 1 -1 1 -1 4.368
## 7 -1 1 1 -1 9.360
## 8 1 1 1 1 15.653
## class=design, type= FrF2DanielPlot(des,half=TRUE)
model <- aov(des)
summary(model)## Number of observations used: 8
## Formula:
## obs ~ (A + B + C + D)^2
## Df Sum Sq Mean Sq
## A 1 18.13 18.13
## B 1 32.18 32.18
## C 1 23.89 23.89
## D 1 51.03 51.03
## A:B 1 6.73 6.73
## A:C 1 25.96 25.96
## A:D 1 0.30 0.30Based on these results none of the effects seem to be significant.
8.24
des1 <- FrF2(nruns = 16, nfactors = 5,resolution = 5, randomize = FALSE, blocks = 2, alias.block.2fis = TRUE, alias.info = 3)
print(des1)## run.no run.no.std.rp Blocks A B C D E
## 1 1 5.1.1 1 -1 1 -1 -1 -1
## 2 2 6.1.2 1 -1 1 -1 1 1
## 3 3 7.1.3 1 -1 1 1 -1 1
## 4 4 8.1.4 1 -1 1 1 1 -1
## 5 5 9.1.5 1 1 -1 -1 -1 -1
## 6 6 10.1.6 1 1 -1 -1 1 1
## 7 7 11.1.7 1 1 -1 1 -1 1
## 8 8 12.1.8 1 1 -1 1 1 -1
## run.no run.no.std.rp Blocks A B C D E
## 9 9 1.2.1 2 -1 -1 -1 -1 1
## 10 10 2.2.2 2 -1 -1 -1 1 -1
## 11 11 3.2.3 2 -1 -1 1 -1 -1
## 12 12 4.2.4 2 -1 -1 1 1 1
## 13 13 13.2.5 2 1 1 -1 -1 1
## 14 14 14.2.6 2 1 1 -1 1 -1
## 15 15 15.2.7 2 1 1 1 -1 -1
## 16 16 16.2.8 2 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frameb <- design.info(design = des1)
print(b$aliased.with.blocks)## [1] "AB" "CDE"Both AB and CDE interactions are confonded within the blocks.
8.25
des2 <- FrF2(nruns = 32, nfactors = 7,resolution = 4, randomize = TRUE, blocks = 4, alias.block.2fis = TRUE, block.old = FALSE, alias.info = 3)
print(des2)## run.no run.no.std.rp Blocks A B C D E F G
## 1 1 13.1.1 1 -1 1 1 -1 -1 -1 -1
## 2 2 16.1.4 1 -1 1 1 1 1 -1 -1
## 3 3 18.1.6 1 1 -1 -1 -1 1 1 1
## 4 4 15.1.3 1 -1 1 1 1 -1 -1 1
## 5 5 17.1.5 1 1 -1 -1 -1 -1 1 -1
## 6 6 14.1.2 1 -1 1 1 -1 1 -1 1
## 7 7 19.1.7 1 1 -1 -1 1 -1 1 1
## 8 8 20.1.8 1 1 -1 -1 1 1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 9 9 21.2.5 2 1 -1 1 -1 -1 -1 -1
## 10 10 12.2.4 2 -1 1 -1 1 1 1 -1
## 11 11 10.2.2 2 -1 1 -1 -1 1 1 1
## 12 12 22.2.6 2 1 -1 1 -1 1 -1 1
## 13 13 24.2.8 2 1 -1 1 1 1 -1 -1
## 14 14 11.2.3 2 -1 1 -1 1 -1 1 1
## 15 15 23.2.7 2 1 -1 1 1 -1 -1 1
## 16 16 9.2.1 2 -1 1 -1 -1 -1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 17 17 28.3.8 3 1 1 -1 1 1 -1 1
## 18 18 27.3.7 3 1 1 -1 1 -1 -1 -1
## 19 19 6.3.2 3 -1 -1 1 -1 1 1 -1
## 20 20 5.3.1 3 -1 -1 1 -1 -1 1 1
## 21 21 8.3.4 3 -1 -1 1 1 1 1 1
## 22 22 25.3.5 3 1 1 -1 -1 -1 -1 1
## 23 23 7.3.3 3 -1 -1 1 1 -1 1 -1
## 24 24 26.3.6 3 1 1 -1 -1 1 -1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 25 25 32.4.8 4 1 1 1 1 1 1 1
## 26 26 31.4.7 4 1 1 1 1 -1 1 -1
## 27 27 2.4.2 4 -1 -1 -1 -1 1 -1 -1
## 28 28 4.4.4 4 -1 -1 -1 1 1 -1 1
## 29 29 30.4.6 4 1 1 1 -1 1 1 -1
## 30 30 1.4.1 4 -1 -1 -1 -1 -1 -1 1
## 31 31 3.4.3 4 -1 -1 -1 1 -1 -1 -1
## 32 32 29.4.5 4 1 1 1 -1 -1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data framea <- design.info(design = des2)
print(a$aliased.with.blocks)## [1] "AB" "AC" "AF" "BC" "BF" "CF" "DEG"As these results shows, the two term interactions AB, AC, AF, BC, BF, CF, DEG, and the three term interaction DEG are confonded to the blocks.
8.28
a)
They used a \(2^{6-2}_{IV}\) design.
b)
des4 <- FrF2(nfactors = 6,resolution = 4,randomize = FALSE, alias.info = 3, alias.block.2fis = TRUE)
aliasprint(des4)## $legend
##
## A=A B=B C=C D=D E=E F=F
##
## $aliases
##
## A=BCE=BDF = B=ACE=ADF = C=ABE=DEF = D=ABF=CEF = E=ABC=CDF = F=ABD=CDE
## AB=CE=DF = AC=BE = AD=BF = AE=BC = AF=BD = CD=EF = CF=DE
## ACD=AEF=BCF=BDE = ACF=ADE=BCD=BEF