Probelm 7.12
replicates<-c(10,0,4,0,0,5,6.5,16.5,4.5,19.5,15,41.5,8,21.5,0,18,18,16.5,6,10,0,20.5,18.5,4.5,18,18,16,39,4.5,10.5,0,5,14,4.5,1,34,18.5,18,7.5,0,14.5,16,8.5,6.5,6.5,6.5,0,7,12.5,17.5,14.5,11,19.5,20,6,23.5,10,5.5,0,3.5,10,0,4.5,10,19.0,20.5,12,25.5,16,29.5,0,8,0,10,0.5,7,13,15.5,1,32.5,16,17.5,14,21.5,15,19,10,8,17.5,7,9,8.5,41,24,4,18.5,18.5,33,5,0,11,10,0,8,6,36,3,36,14,16,6.5,8)
length <- rep(c(-1,1,-1,1),28)
type <- rep(c(-1,-1,1,1),28)
brk <- rep(c(-1,-1,-1,-1,1,1,1,1),14)
slope <- c(rep(-1,8),rep(1,8))
slope <- rep(slope,7)
block<-c(rep(1,16),rep(2,16),rep(3,16),rep(4,16),rep(5,16),rep(6,16),rep(7,16))
dat<-data.frame(replicates,length,type,brk,slope)
model<-aov(replicates~length*type*brk*slope+block,data = dat)
summary(model)
## Df Sum Sq Mean Sq F value Pr(>F)
## length 1 917 917.1 10.673 0.00151 **
## type 1 388 388.1 4.517 0.03616 *
## brk 1 145 145.1 1.689 0.19687
## slope 1 1 1.4 0.016 0.89888
## block 1 152 152.1 1.769 0.18663
## length:type 1 219 218.7 2.545 0.11398
## length:brk 1 12 11.9 0.138 0.71068
## type:brk 1 115 115.0 1.338 0.25020
## length:slope 1 94 93.8 1.092 0.29877
## type:slope 1 56 56.4 0.657 0.41976
## brk:slope 1 2 1.6 0.019 0.89084
## length:type:brk 1 7 7.3 0.084 0.77206
## length:type:slope 1 113 113.0 1.315 0.25437
## length:brk:slope 1 39 39.5 0.459 0.49952
## type:brk:slope 1 34 33.8 0.393 0.53224
## length:type:brk:slope 1 96 95.6 1.113 0.29411
## Residuals 95 8164 85.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
From the ANOVA table we can see that the p value for blocking is more than 0.05, so we can say that blocking is insignificant.
Probelm 7.20
In this probelm we can confound on ABCE,ABDF,CDEF of 2^6 factorial design in four blocks
Here after multiplying ABCE and ABDF we get CDEF
b1 <- c('a','b','cd','abcd','ace','bce','de','abde','cf','abcf','adf','bdf','ef','abef','acdef','bcdef')
b2 <- c('c','abc','ad','bd','e','abe','acde','bcde','af','bf','cdf','abcdf','acef','bcef','def','abdef')
b3 <- c('ac','bc','d','abd','ae','be','cde','abcde','f','abf','acdf','bcdf','cef','abcef','adef','bdef')
b4 <- c('1','ab','acd','bcd','ce','abce','ade','bde','acf','bcf','df','abdf','aef','bef','cdef','abcdef')
Probelm 7.21
blk1 <- c('b','acd','ce','abde','abcf','df','aef','bcdef')
blk2 <- c('abc','d','ae','bcde','bf','acdf','cef','abdef')
blk3 <- c('a','bcd','abce','de','cf','abdf','bef','acdef')
blk4 <- c('c','abd','be','acde','af','bcdf','abcef','def')
blk5<- c('ac','bd','abe','cde','f','abcdf','bcef','adef')
blk6<- c('1','abcd','bce','ade','acf','bdf','abef','cdef')
blk7<- c('bc','ad','e','abcde','abf','cdf','acef','bdef')
blk8<- c('ab','cd','ace','bde','bcf','adf','ef','abcdef')
In this probelm the factors that are confounded with blocks are ABCD, ABEF, ACE, BDE, CDEF, BCF and ADF