Three general methods for covariance analysis of categorical data are reviewed and applied to an example from a clinical trial in rheumatoid arthritis. The three methods considered are randomization-model nonparametric procedures, maximum likelihood logistic regression, and weighted least squares analysis of correlated marginal functions. A fourth heuristic approach, the unweighted linear model analysis, is an approximate procedure but it is easy to implement. The assumptions and statistical issues for each method are discussed so as to emphasize philosophical differences between their rationales. Attention is given to computational differences, but it is shown that the methods lead to similar results for analogous problems. It is argued that the essential differences between the methods lie in their underlying assumptions and the generality of the conclusions which may be drawn.