  Cohen's kappa is a useful measure for agreement between the judges,
inter-rater reliability, and also goodness of fit in classification problems.
For binary nominal and ordinal data, kappa and correlation are equally
applicable. We have found a linear relationship between correlation and kappa
for binary data. Exact bounds of kappa are much more important as kappa can be
only .5 even if there is very strong agreement. The exact upper bound was
developed by Cohen (1960) but the exact lower bound is also important if the
range of kappa is small for some marginals. We have developed an algorithm to
find the exact lower bound given marginal proportions. Our final contribution
is a method to generate multivariate nominal and ordinal data with a specified
kappa matrix based on the rearrangement of independently generated marginal
data to a multidimensional contingency table, where cell counts are found by
solving system of linear equations for positive roots.
