> #2.3 The Untied Analysis
> #Without ties there is no difference between using the natural and mid-rank scores
> 
> Nij<-rbind(
+ c( 1, 1, 1, 1, 0, 0, 0, 0, 0, 0),
+ c( 0, 0, 0, 0, 1, 0, 0, 1, 1, 0),
+ c( 0, 0, 0, 0, 0, 1, 1, 0, 0, 1))
> rownames(Nij)<-c("A","B","C")
> colnames(Nij)<-1:10
> Nij
  1 2 3 4 5 6 7 8 9 10
A 1 1 1 1 0 0 0 0 0  0
B 0 0 0 0 1 0 0 1 1  0
C 0 0 0 0 0 1 1 0 0  1
> CRD(Nij) #default analysis is to use mid-rank scores
$Cri
   
     Location Dispersion    Skewness   Kurtosis 5-th order  6-th order  7-th order 8-th order 9-th order
  A -1.981735  0.5222330  0.61536276 -0.5048714 -0.2148345  0.46709937 -0.05269379 -0.3926777  0.3809534
  B  1.048809 -0.4522670 -0.69186077 -0.6801378 -1.1783300 -0.60677988  0.96338777  0.8744629 -0.7776575
  C  1.239501 -0.1507557 -0.01869894  1.2631130  1.4263994  0.06741999 -0.90254223 -0.4210377  0.3377704

$partition
         df        SS     pvalue
Location  2  6.563636 0.03755990
Residual 16 11.436364 0.78178402
Total    18 18.000000 0.45565260

> CRD(Nij,rankscores=F) #force code not (F=false) to use mid-rank scores so to use natural scores instead
$Cri
   
     Location Dispersion    Skewness   Kurtosis 5-th order  6-th order  7-th order 8-th order 9-th order
  A -1.981735  0.5222330  0.61536276 -0.5048714 -0.2148345  0.46709937 -0.05269379 -0.3926777  0.3809534
  B  1.048809 -0.4522670 -0.69186077 -0.6801378 -1.1783300 -0.60677988  0.96338777  0.8744629 -0.7776575
  C  1.239501 -0.1507557 -0.01869894  1.2631130  1.4263994  0.06741999 -0.90254223 -0.4210377  0.3377704

$partition
         df        SS     pvalue
Location  2  6.563636 0.03755990
Residual 16 11.436364 0.78178402
Total    18 18.000000 0.45565260

>