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A new approach to distribution free tests in contingency tables

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  • Thuong T. M. Nguyen

    (Victoria University of Wellington)

Abstract

We suggest an extremely wide class of asymptotically distribution free goodness of fit tests for testing independence in two-way contingency tables, or equivalently, independence of two discrete random variables. The nature of these tests is that the test statistics can be viewed as definite functions of the transformation of $$\widehat{T}_n = (\widehat{T}_{ij})=\Big (\frac{\nu _{ij}- n\hat{a}_i\hat{b}_j}{\sqrt{n\hat{a}_i\hat{b}_j}}\Big )$$ T ^ n = ( T ^ i j ) = ( ν i j - n a ^ i b ^ j n a ^ i b ^ j ) where $$\nu _{ij}$$ ν i j are frequencies and $$\hat{a}_i, \hat{b}_j$$ a ^ i , b ^ j are estimated marginal distributions. Our method is also applicable for testing independence of two discrete random vectors. We make some comparisons on statistical powers of the new tests with the conventional chi-square test and suggest some cases in which this class is significantly more powerful.

Suggested Citation

  • Thuong T. M. Nguyen, 2017. "A new approach to distribution free tests in contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 153-170, February.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:2:d:10.1007_s00184-016-0596-6
    DOI: 10.1007/s00184-016-0596-6
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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
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    Cited by:

    1. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.
    2. Khmaladze, Estate, 2017. "Distribution free testing for conditional distributions given covariates," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 348-354.
    3. Roberts, Leigh A., 2019. "Distribution free goodness of fit testing of grouped Bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 47-53.

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