On the use of ridit analysis

Ridit analysis is statistical method for comparing ordinal-scale responses. In this paper, the extact variance and asymptotic distribution of the average ridit is developed, including the cases in which the reference group is sampled or the comparison group is finite. The appropriate use and interpretation of ridit analysis is also discussed.The authors wish to thank Andrew Klugh for this support, and the references and David Feigenbaum for their very helpful comments.     

Matrices with a given number of violations of Regular Minimality

A row (or column) of an n×n matrix complies with Regular Minimality (RM) if it has a unique minimum entry which is also a unique minimum entry in its column (respectively, row). The number of violations of RM in a matrix is defined as the number of rows (equivalently, columns) that do not comply with RM. We derive a formula for the proportion of n×n matrices with a given number of violations of RM among all n×n matrices with no tied entries. The proportion of matrices with no more than a given number of violations can be treated as the p-value of a permutation test whose null hypothesis states that all permutations of the entries of a matrix without ties are equiprobable, and the alternative hypothesis states that RM violations occur with lower probability than predicted by the null hypothesis. A matrix with ties is treated as being represented by all matrices without ties that have the same set of strict inequalities among their entries.