####################################Chapter 23, TA01, unbalanced design###############################
growth<-read.table("~/Desktop/jenn/teaching/stat445545/data/CH23TA01.txt",col.names=c("y","A","B","obs"))
n<-nrow(growth)
n
## [1] 14
growth
## y A B obs
## 1 1.4 1 1 1
## 2 2.4 1 1 2
## 3 2.2 1 1 3
## 4 2.1 1 2 1
## 5 1.7 1 2 2
## 6 0.7 1 3 1
## 7 1.1 1 3 2
## 8 2.4 2 1 1
## 9 2.5 2 2 1
## 10 1.8 2 2 2
## 11 2.0 2 2 3
## 12 0.5 2 3 1
## 13 0.9 2 3 2
## 14 1.3 2 3 3
growth$A<-factor(growth$A)
growth$B<-factor(growth$B)
attach(growth)
#summary statistics
tapply(y,A,mean) #row means
## 1 2
## 1.657143 1.628571
tapply(y,B, mean) #column means
## 1 2 3
## 2.10 2.02 0.90
aggregate(y~A*B, data=growth,mean) #cell means
## A B y
## 1 1 1 2.0
## 2 2 1 2.4
## 3 1 2 1.9
## 4 2 2 2.1
## 5 1 3 0.9
## 6 2 3 0.9
aggregate(y~A*B, data=growth,length) #cell size, unequal
## A B y
## 1 1 1 3
## 2 2 1 1
## 3 1 2 2
## 4 2 2 3
## 5 1 3 2
## 6 2 3 3
##View interaction plots, also called profile plots, page 955
interaction.plot(B,A,y,type='b',
col=1:2, pch=1:2)
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)
#full model
#adding restrictions, A=contr.sum,B=contr.sum
myfit<-lm(y~A+B+A:B,contrasts = c(A=contr.sum,B=contr.sum))
## The contrast statement above must be included identifying
## each main effect with "contr.sum" in order for the correct
## Type III SS to be computed.
#without restriction
myfitwot<-lm(y~A+B+A:B)
#type I
anova(myfit) #type I SS
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 0.0029 0.00286 0.0176 0.897785
## B 2 4.3960 2.19800 13.5262 0.002713 **
## A:B 2 0.0754 0.03771 0.2321 0.798034
## Residuals 8 1.3000 0.16250
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(myfitwot) #type I SS
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 0.0029 0.00286 0.0176 0.897785
## B 2 4.3960 2.19800 13.5262 0.002713 **
## A:B 2 0.0754 0.03771 0.2321 0.798034
## Residuals 8 1.3000 0.16250
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
library(car)
## Loading required package: carData
#type III
Anova(myfit,type=3) #type III SS
## Anova Table (Type III tests)
##
## Response: y
## Sum Sq Df F value Pr(>F)
## (Intercept) 34.680 1 213.4154 4.729e-07 ***
## A 0.120 1 0.7385 0.415160
## B 4.190 2 12.8914 0.003145 **
## A:B 0.075 2 0.2321 0.798034
## Residuals 1.300 8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(myfitwot,type=3) #type III SS
## Anova Table (Type III tests)
##
## Response: y
## Sum Sq Df F value Pr(>F)
## (Intercept) 12.0000 1 73.8462 2.6e-05 ***
## A 0.1200 1 0.7385 0.41516
## B 1.6171 2 4.9758 0.03944 *
## A:B 0.0754 2 0.2321 0.79803
## Residuals 1.3000 8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#reduced model
myfit2<-lm(y~A+B,contrasts = c(A=contr.sum,B=contr.sum))
anova(myfit2) #type I SS
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 0.0029 0.00286 0.0208 0.8882630
## B 2 4.3960 2.19800 15.9805 0.0007687 ***
## Residuals 10 1.3754 0.13754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(myfit2,type=3) #type III SS
## Anova Table (Type III tests)
##
## Response: y
## Sum Sq Df F value Pr(>F)
## (Intercept) 38.855 1 282.493 1.166e-08 ***
## A 0.093 1 0.673 0.4311159
## B 4.396 2 15.980 0.0007687 ***
## Residuals 1.375 10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
####################################Bakery data, balanced design###############################
bakery<- read.table(file="~/Desktop/jenn/teaching/stat445545/data/CH19TA07.txt",col.names=c("y","height","width","obs"))
nt<-nrow(bakery)
nt
## [1] 12
attach(bakery)
## The following objects are masked from growth:
##
## obs, y
bakery
## y height width obs
## 1 47 1 1 1
## 2 43 1 1 2
## 3 46 1 2 1
## 4 40 1 2 2
## 5 62 2 1 1
## 6 68 2 1 2
## 7 67 2 2 1
## 8 71 2 2 2
## 9 41 3 1 1
## 10 39 3 1 2
## 11 42 3 2 1
## 12 46 3 2 2
height<-factor(height)
width<-factor(width)
aggregate(y~height*width, data=bakery,length) #cell size, balanced design
## height width y
## 1 1 1 2
## 2 2 1 2
## 3 3 1 2
## 4 1 2 2
## 5 2 2 2
## 6 3 2 2
myfitbakery<-lm(y~height+width+height*width,contrasts = c(height=contr.sum,width=contr.sum))
anova(myfitbakery) #Type I SS
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## height 2 1544 772.00 74.7097 5.754e-05 ***
## width 1 12 12.00 1.1613 0.3226
## height:width 2 24 12.00 1.1613 0.3747
## Residuals 6 62 10.33
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(myfitbakery,type=2) #Type II SS
## Anova Table (Type II tests)
##
## Response: y
## Sum Sq Df F value Pr(>F)
## height 1544 2 74.7097 5.754e-05 ***
## width 12 1 1.1613 0.3226
## height:width 24 2 1.1613 0.3747
## Residuals 62 6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(myfitbakery,type=3) #Type III SS
## Anova Table (Type III tests)
##
## Response: y
## Sum Sq Df F value Pr(>F)
## (Intercept) 31212 1 3020.5161 2.437e-09 ***
## height 1544 2 74.7097 5.754e-05 ***
## width 12 1 1.1613 0.3226
## height:width 24 2 1.1613 0.3747
## Residuals 62 6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#type I, II, and III SS are all the same