RBD

This is a solved problem from the text book titled “Statistics for Business and Economics” by Anderson and Sweeny

#Andersen Sweeny Problem
df2 = read.table("ATC_Stress_Test.txt", header=TRUE); df2 
##   System_A System_B System_C
## 1       15       15       18
## 2       14       14       14
## 3       10       11       15
## 4       13       12       17
## 5       16       13       16
## 6       13       13       13
r = c(t(as.matrix(df2))) # response data 
r
##  [1] 15 15 18 14 14 14 10 11 15 13 12 17 16 13 16 13 13 13
f = c("System_A", "System_B", "System_C")   # treatment levels 

k = 3                    # number of treatment levels 
n = 6                    # number of control blocks

tm = gl(k, 1, n*k, factor(f))   # matching treatment 
tm
##  [1] System_A System_B System_C System_A System_B System_C System_A System_B
##  [9] System_C System_A System_B System_C System_A System_B System_C System_A
## [17] System_B System_C
## Levels: System_A System_B System_C
blk = gl(n, k, k*n)             # blocking factor 

blk
##  [1] 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
## Levels: 1 2 3 4 5 6
av = aov(r ~ tm + blk)

summary(av) 
##             Df Sum Sq Mean Sq F value Pr(>F)  
## tm           2     21    10.5   5.526 0.0242 *
## blk          5     30     6.0   3.158 0.0574 .
## Residuals   10     19     1.9                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1