Tests of independence for ordinal data using bootstrap

In a two-way cross table, the association between two ordinal variables can be assessed by different measures such as Goodman and Kruskal's gamma (γ) and Kendall's tau-b (τ_b). When sample size is large, the independence hypothesis between the row and the column variables can be tested by the traditional asymptotic test (TAT). TAT, however, fails to work satisfactorily when sample size is small because the theoretical distribution of the test statistic may only hold asymptotically. In this study, two bootstrap-based tests (BBTs) are proposed for testing the independence hypothesis. Monte Carlo studies are used to compare the TAT with the BBTs at small to moderate sample sizes. The BBTs are superior to the TAT in two aspects: The control of Type I error rate by the BBTs is more accurate, and the BBTs are more powerful because they are more likely than the TAT to reject false null hypotheses.