Example R programs and commands
                       17. Kendall's Rank Concordance

# All lines preceded by the "#" character are my comments.
# All other left-justified lines are my input.
# All other indented lines are the R program output.

# Kendall's W, or rank concordance statistic, is not computed by any
# function in R's basic statistics package.  It is available as a 
# contributed function, which I have placed on the class web site.
#
# Input the definition of kendall.w() by cutting and pasting from
#
#   http://www.math.wustl.edu/~victor/classes/ma322/kendall.w.R
# 
# (You may need to cut and paste in several pieces.)


# Read some rank data:
# Paper: 1     2        3       4   
# ----------------------------------
data<-scan()
        4       3       2       1   
        3       4       2       1   
        4       3       1       2   
        3       4       1       2   
        4       2       1       3   
        4       2       3       1   

dim(data)<-c(4,6)   # Coerce the data into a 4x6 matrix, TRANSPOSED!
x <- t(data)        # Un-transpose so that the rows have equal sums.

# Call the contributed function, specifying that the numbers in the
# matrix x are ranks:
kendall.w( x, ranks=TRUE )

  Kendall's W for ordinal data
  W = 0.6  p(table)  <0.01