Objective: To explore several numerical methods of ordinal variable in one-way ordinal contingency table and their interrelationship, and to compare corresponding statistical analysis methods such as Ridit analysis and rank sum test.
Methods: Formula deduction was based on five simplified grading approaches including rank_r(i), ridit_r(i), ridit_r(ci), ridit_r(mi), and table scores. Practical data set was verified by SAS8.2 in clinical practice (to test the effect of Shiwei solution in treatment for chronic tracheitis).
Results: Because of the linear relationship of rank_r(i) = N ridit_r(i) + 1/2 = N ridit_r(ci) = (N + 1) ridit_r(mi), the exact chi2 values in Ridit analysis based on ridit_r(i), ridit_r(ci), and ridit_r(mi), were completely the same, and they were equivalent to the Kruskal-Wallis H test. Traditional Ridit analysis was based on ridit_r(i), and its corresponding chi2 value calculated with an approximate variance (1/12) was conservative. The exact chi2 test of Ridit analysis should be used when comparing multiple groups in the clinical researches because of its special merits such as distribution of mean ridit value on (0,1) and clear graph expression. The exact chi2 test of Ridit analysis can be output directly by proc freq of SAS8.2 with ridit and modridit option (SCORES =).
Conclusion: The exact chi2 test of Ridit analysis is equivalent to the Kruskal-Wallis H test, and should be used when comparing multiple groups in the clinical researches.