> #6.2 Wine Example
> x<-rbind(
+ c(2,3.5,3.5,2,2),
+ c(1.5,4,1.5,4,4),
+ c(2,3.5,2,3.5,2),
+ c(2,3.5,3.5,2,2),
+ c(4,4,4,1.5,1.5),
+ c(2,3.5,3.5,2,2),
+ c(2,3.5,3.5,2,2),
+ c(2.5,5,2.5,2.5,2.5),
+ c(2,3.5,3.5,2,2),
+ c(1.5,4,4,4,1.5))
> colnames(x)<-c("A","B","C","D","E")
> 
> #Have to get ranks from x*10 as xtotab assumes integer
> xtotab(x*10)
         1        2        3         4         5
A 3.250000 3.250000 2.583333 0.5833333 0.3333333
B 0.000000 0.000000 1.000000 4.0000000 5.0000000
C 1.083333 1.083333 1.250000 3.4166667 3.1666667
D 2.416667 2.416667 2.583333 1.4166667 1.1666667
E 3.250000 3.250000 2.583333 0.5833333 0.3333333
> U(x*10)
     1    2    3    4 5
1 3.75 3.75 2.25 0.25 0
2 3.75 3.75 2.25 0.25 0
3 2.25 2.25 3.25 1.25 1
4 0.25 0.25 1.25 4.25 4
5 0.00 0.00 1.00 4.00 5
> BlockAnalysis(x*10)
$Cri
    Location Dispersion
A -1.9965487 -0.2287173
B  3.2884332  0.9863435
C  1.5267726  0.2358648
D -0.8221083 -0.7647736
E -1.9965487 -0.2287173

$partition
           df        SS       pvalue
Location    4 21.793103 0.0002203478
Dispersion  4  1.718008 0.7874439687
Residual    4  2.044444 0.7275844491
Total      12 25.555556 0.0123989048

> 
> #Note that 4 degrees of freedom have been lost - the total degrees of freedom
> #is usually (number of products - 1)^2, which is (5-1)^2=16 here
> 
> #This is because U(x*10) is not of full rank (see the discussion at the end of chapter 3.6)
> eigen(U(x*10))$values
[1]  1.000000e+01  8.085927e+00  1.335151e+00  5.789217e-01 -6.802794e-16
> det(U(x*10))
[1] 0
>