Question No: 7.12
Entering the dataโฆ
A<-c(rep(c(rep(-1,7), rep(1, 7)), 8))
B<-c(rep(c(rep(-1,14), rep(1, 14)), 4))
C<-c(rep(c(rep(-1,28), rep(1, 28)), 2))
D<-c(rep(-1, 56), rep(1, 56))
block<-c(rep(seq(1,7), 16))
obs1<-c(10.0, 18.0, 14.0, 12.5, 19.0, 16.0, 18.5, 0.0, 16.5, 4.5, 17.5, 20.5, 17.5, 33.0,
4.0, 6.0, 1.0, 14.5, 12.0, 14.0, 5.0, 0.0, 10.0, 34.0, 11.0, 25.5, 21.5, 0.0,
0.0, 0.0, 18.5, 19.5, 16.0, 15.0, 11.0, 5.0, 20.5, 18.0, 20.0, 29.5, 19.0, 10.0,
6.5, 18.5, 7.5, 6.0, 0.0, 10.0, 0.0, 16.5, 4.5, 0.0, 23.5, 8.0, 8.0, 8.0,
4.5, 18.0, 14.5, 10.0, 0.0, 17.5, 6.0, 19.5, 18.0, 16.0, 5.5, 10.0, 7.0, 36.0,
15.0, 16.0, 8.5, 0.0, 0.5, 9.0, 3.0, 41.5, 39.0, 6.5, 3.5, 7.0, 8.5, 36.0,
8.0, 4.5, 6.5, 10.0, 13.0, 41.0, 14.0, 21.5, 10.5, 6.5, 0.0, 15.5, 24.0, 16.0,
0.0, 0.0, 0.0, 4.5, 1.0, 4.0, 6.5, 18.0, 5.0, 7.0, 10.0, 32.5, 18.5, 8.0)
A<-as.factor(A)
B<-as.factor(B)
C<-as.factor(C)
D<-as.factor(D)
block<-as.factor(block)ANOVA (With Blocking)
model1<- aov(obs1 ~ A*B*C*D + block)
summary(model1)## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 917 917.1 10.396 0.00176 **
## B 1 388 388.1 4.400 0.03875 *
## C 1 145 145.1 1.645 0.20290
## D 1 1 1.4 0.016 0.90021
## block 6 376 62.7 0.710 0.64202
## A:B 1 219 218.7 2.479 0.11890
## A:C 1 12 11.9 0.135 0.71433
## B:C 1 115 115.0 1.304 0.25655
## A:D 1 94 93.8 1.063 0.30522
## B:D 1 56 56.4 0.640 0.42594
## C:D 1 2 1.6 0.018 0.89227
## A:B:C 1 7 7.3 0.082 0.77499
## A:B:D 1 113 113.0 1.281 0.26073
## A:C:D 1 39 39.5 0.448 0.50520
## B:C:D 1 34 33.8 0.383 0.53767
## A:B:C:D 1 96 95.6 1.084 0.30055
## Residuals 90 7940 88.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANOVA (Without Blocking)
model2<- aov(obs1 ~ A*B*C*D)
summary(model2)## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 917 917.1 10.588 0.00157 **
## B 1 388 388.1 4.481 0.03686 *
## C 1 145 145.1 1.676 0.19862
## D 1 1 1.4 0.016 0.89928
## A:B 1 219 218.7 2.525 0.11538
## A:C 1 12 11.9 0.137 0.71178
## B:C 1 115 115.0 1.328 0.25205
## A:D 1 94 93.8 1.083 0.30066
## B:D 1 56 56.4 0.651 0.42159
## C:D 1 2 1.6 0.019 0.89127
## A:B:C 1 7 7.3 0.084 0.77294
## A:B:D 1 113 113.0 1.305 0.25623
## A:C:D 1 39 39.5 0.456 0.50121
## B:C:D 1 34 33.8 0.390 0.53386
## A:B:C:D 1 96 95.6 1.104 0.29599
## Residuals 96 8316 86.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Conclusion: From ANOVA summary of blocked and unblocked design, the p-values of blocked and unblocked designs are nearly same and not deviate too much.