Kendall's tau is a widely used rank correlation coefficient.
Assessing independence in data is crucial for statistical analysis.
Purpose of the Study:
To introduce and evaluate a two-stage analog of Kendall's distribution-free test for independence.
To provide critical values for hypothesis testing.
Main Methods:
Development of a two-stage test statistic.
Derivation of the null-limiting joint distribution.
Monte Carlo simulations to assess distribution usefulness and test power.
Main Results:
The null-limiting joint distribution of the two-stage test statistics is bivariate normal.
Critical values for common significance levels (alpha = .01, .05, .10) are provided.
Monte Carlo studies confirmed the utility of the limiting distribution for small samples and showed comparable power to the single-stage test with fewer samples.
Conclusions:
The two-stage Kendall's test offers an efficient alternative to the traditional single-stage test.
The derived critical values and demonstrated performance make it a practical tool for independence testing.