The following R code analyzes the yield dataset for a 5x5 Latin Square design by creating the yield dataset as a data frame, y, and then fitting a linear model using the lm() function to the data. This analyzes the yield in terms of the row, column and treatment effects and produces a summary table. The anova() statement performs the ANOVA, which we then display in table form (note that R does not display the totals row). The two matrix() functions display the design matrix and the data matrix in 5x5 format, as illustrated.
R Code
## setup framework for rows, columns and treatments
rows<- c(rep("r1",1), rep("r2",1), rep("r3",1), rep("r4",1), rep("r5",1))
cols<- c(rep("cA",5), rep("cB",5), rep("cC",5), rep("cD",5), rep("cE",5))
treatments<- c("A","C","D","E","B", "D","B","C","A","E", "E","A","B","C","D", "B","E","A","D","C", "C","D","E","B","A")
matrix(y$treatments, 5,5)
## assign data to variable "yield"
yield<- c(7.4,11.8,10.1,8.8,11.8,8.9,6.5,17.9,10.1,8.8,5.8,8.7,9.0,15.7,14.3,12.0,7.6,8.5,11.1,18.4,14.3,7.9,7.1,7.4,10.1)
matrix(y$yield, 5,5)
y<- data.frame(cols,rows,treatments, yield)
## create a 2x2 plot array
par(mfrow=c(2,2))
## generate box plots of yield versus the 3 factors
plot(yield ~ rows+cols+treatments,y)
## apply a linear model
yfit <- lm(yield ~ rows+cols+treatments, y)
## compute the analysis of variance table
anova(yfit)
Matrix outputs:
[,1] [,2] [,3] [,4] [,5]
[1,] "A" "D" "E" "B" "C"
[2,] "C" "B" "A" "E" "D"
[3,] "D" "C" "B" "A" "E"
[4,] "E" "A" "C" "D" "B"
[5,] "B" "E" "D" "C" "A"
[,1] [,2] [,3] [,4] [,5]
[1,] 7.4 8.9 5.8 12.0 14.3
[2,] 11.8 6.5 8.7 7.6 7.9
[3,] 10.1 17.9 9.0 8.5 7.1
[4,] 8.8 10.1 15.7 11.1 7.4
[5,] 11.8 8.8 14.3 18.4 10.1
Plot output
