Tests of independence for ordinal data using bootstrap

Wai Chan*, Yiu Fai Yung, Peter M. Bentler, Man Lai TANG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)


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 (τb). 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.

Original languageEnglish
Pages (from-to)221-240
Number of pages20
JournalEducational and Psychological Measurement
Issue number2
Publication statusPublished - Apr 1998

Scopus Subject Areas

  • Education
  • Developmental and Educational Psychology
  • Applied Psychology
  • Applied Mathematics


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