The methods and application for analyzing categorical ordinal data have matured in statistical inferences during recent decades of development. The methods include logistic regression models, odds ratios, inferential methods by using chi-squared tests of independence and conditional independence. On the basis, this thesis presents an analysis of equality of dependent correlations with the longitudinal ordinal vari- able. Eight test statistics, Dunn and Clark's Z, Steriger's Z, Meng's Z, Hitter's Z, Hotelling's t, William's t and William's modified t per Hendrickson, for comparing dependent correlations are presented. The results via simulation studies indicate that the choice as to which test statistics is relatively optimal, in terms of empirical level and statistical power, depends not only on sample size but also on the magnitude of the correlations and the effect size. On the other hand, this thesis suggests the meth- ods of modification for some statistical tests when they performed unsatisfactory with ordinal variables. The thesis also brie y discusses practicing the relatively efficient test statistics for testing equality of the correlation coefficients in real medical data and has achieved the good results.