## question 7.12
LOP<-c(rep(c(rep(-1,7), rep(1, 7)), 8))
TOP<-c(rep(c(rep(-1,14), rep(1, 14)), 4))
BOP<-c(rep(c(rep(-1,28), rep(1, 28)), 2))
SOP<-c(rep(-1, 56), rep(1, 56))
block<-c(rep(seq(1,7), 16))
response<-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)
library(GAD)## Loading required package: matrixStats## Loading required package: R.methodsS3## R.methodsS3 v1.8.1 (2020-08-26 16:20:06 UTC) successfully loaded. See ?R.methodsS3 for help.LOP<-as.fixed(LOP)
TOP<-as.fixed(TOP)
BOP<-as.fixed(BOP)
SOP<-as.fixed(SOP)
block<-as.random(block)
dat<-data.frame(LOP,TOP,BOP,SOP,response)
## anova test without blocking
model<- aov(response ~ LOP*TOP*BOP*SOP)
summary(model)## Df Sum Sq Mean Sq F value Pr(>F)
## LOP 1 917 917.1 10.588 0.00157 **
## TOP 1 388 388.1 4.481 0.03686 *
## BOP 1 145 145.1 1.676 0.19862
## SOP 1 1 1.4 0.016 0.89928
## LOP:TOP 1 219 218.7 2.525 0.11538
## LOP:BOP 1 12 11.9 0.137 0.71178
## TOP:BOP 1 115 115.0 1.328 0.25205
## LOP:SOP 1 94 93.8 1.083 0.30066
## TOP:SOP 1 56 56.4 0.651 0.42159
## BOP:SOP 1 2 1.6 0.019 0.89127
## LOP:TOP:BOP 1 7 7.3 0.084 0.77294
## LOP:TOP:SOP 1 113 113.0 1.305 0.25623
## LOP:BOP:SOP 1 39 39.5 0.456 0.50121
## TOP:BOP:SOP 1 34 33.8 0.390 0.53386
## LOP:TOP:BOP:SOP 1 96 95.6 1.104 0.29599
## Residuals 96 8316 86.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##From the ANOVA test we can see that lop and top are not significant. The p-value for length is0.00157 and type is 0.03686 and so we could say that only these factors are significant.
## now we test with LOP and TOP With blocking
## anova test with blocking
model1<- aov(response ~ LOP*TOP* + block)
summary(model1)## Df Sum Sq Mean Sq F value Pr(>F)
## LOP 1 917 917.1 10.273 0.00191 **
## TOP 1 388 388.1 4.348 0.04009 *
## block 6 376 62.7 0.702 0.64870
## LOP:TOP 1 219 218.7 2.450 0.12132
## LOP:block 6 487 81.2 0.910 0.49222
## TOP:block 6 503 83.9 0.940 0.47126
## LOP:TOP:block 6 165 27.4 0.307 0.93149
## Residuals 84 7499 89.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## So, finally after blocking and just running with these two factors we get the p-values for those factors as 0.00191 for LOP and TOP is 0.04009 for type which indicates that they are significant.###source code
LOP<-c(rep(c(rep(-1,7), rep(1, 7)), 8))
TOP<-c(rep(c(rep(-1,14), rep(1, 14)), 4))
BOP<-c(rep(c(rep(-1,28), rep(1, 28)), 2))
SOP<-c(rep(-1, 56), rep(1, 56))
block<-c(rep(seq(1,7), 16))
response<-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)
library(GAD)
LOP<-as.fixed(LOP)
TOP<-as.fixed(TOP)
BOP<-as.fxed(BOP)
SOP<-as.fixed(SOP)
block<-as.random(block)
dat<-data.frame(LOP,TOP,BOP,SOP,response)
model<- aov(response ~ LOP*TOP*BOP*SOP)
summary(model)
model1<- aov(response ~ LOP*TOP* + block)
summary(model1)