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Two-stage test of independence using Kendall's statistic

J D Spurrier, J E Hewett

    Biometrics
    |September 1, 1980
    PubMed
    Summary

    A novel two-stage Kendall

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    Area of Science:

    • Statistics
    • Nonparametric Statistics

    Background:

    • 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.

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