Viewing the two response variables as two independent ratings of the n subjects, the Kappa coefficient equals +1 when there is complete agreement of the raters. When the observed agreement exceeds chance agreement, the Kappa coefficient is positive, with its magnitude reflecting the strength of agreement. Although unusual in practice, Kappa is negative when the observed agreement is less than chance agreement. The minimum value of Kappa is between -1 and 0, depending on the marginal proportions.

See Cohen (1960) and Fleiss et al. (1969).

For Bowker’s test of symmetry, the null hypothesis is that the probabilities in the two-by-two table satisfy symmetry (pij=pji).