In: Math

Problem 1.

(a) The columns of response and factors can be defined in R as follows, use these codes to solve the problem.

y<-c(2, 3, 10, 12, 8, 4, 11, 8)##response : scores

a<-c("Heart","Heart", "Soul", "Soul","Heart","Heart", "Soul", "Soul")##factor A

b<-c("D", "D", "D", "D", "R", "R", "R", "R")##factor B (group variable)

(b) Find the overall mean, row means, column means, each cell mean for the table given in problem 1.

R code:

y<-c(2, 3, 10, 12, 8, 4, 11, 8)##response : scores

a<-c("Heart","Heart", "Soul", "Soul","Heart","Heart", "Soul", "Soul")##factor A

b<-c("D", "D", "D", "D", "R", "R", "R", "R")##factor B (group
variable)

M=data.frame(cbind(y,a,b))

#overall mean

G=mean(y)

# Row means

Row1=mean(y[1:4])

Row2=mean(y[5:8])

#column means

Column1=mean(c(y[1:2],y[5:6]))

Column2=mean(c(y[3:4],y[7:8]))

#Cell means

Cell_11=mean(y[1:2])

Cell_12=mean(y[3:4])

Cell_21=mean(y[5:6])

Cell_22=mean(y[7:8])

G

Row1

Row2

Column1

Column2

Cell_11

Cell_12

Cell_21

Cell_22

Output:

G

[1] 7.25

> Row1

[1] 6.75

> Row2

[1] 7.75

> Column1

[1] 4.25

> Column2

[1] 10.25

> Cell_11

[1] 2.5

> Cell_12

[1] 11

> Cell_21

[1] 6

> Cell_22

[1] 9.5

Overall mean=7.25

Mean of Row 1 (Level "D" of factor B)= 6.75

Mean of Row 2 (Level "R" of factor B)= 7.75

Mean of Column1 (Level "Heart" of factor A)= 4.25

Mean of Column2 (Level "Soul" of factor A)= 10.25

Mean of Cell (D, Heart)=2.5

Mean of Cell (D, Soul)=11

Mean of Cell (R, Heart)=6

Mean of Cell (R, Soul)= 9.5

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